Moiré-engineered light-matter interactions in MoS2/WSe2 heterobilayers at room temperature
Qiaoling Lin, Hanlin Fang, Alexei Kalaboukhov, Yuanda Liu, Yi Zhang, Moritz Fischer, Juntao Li, Joakim Hagel, Samuel Brem, Ermin Malic, Nicolas Stenger, Zhipei Sun, Martijn Wubs, and Sanshui Xiao
Nature Commun. 15, 8762 (2024)
|
view abstract
Abstract: Moiré superlattices in van der Waals heterostructures represent a highly tunable quantum system, attracting substantial interest in both many-body
physics and device applications. However, the influence of the moiré potential on light-matter interactions at room temperature has remained largely unexplored. In our study, we
demonstrate that the moiré potential in MoS2/WSe2 heterobilayers facilitates the localization of interlayer exciton (IX) at room temperature. By performing reflection contrast
spectroscopy, we demonstrate the importance of atomic reconstruction in modifying intralayer excitons, supported by the atomic force microscopy experiment. When decreasing the twist
angle, we observe that the IX lifetime becomes longer and light emission gets enhanced, indicating that non-radiative decay channels such as defects are suppressed by the moiré
potential. Moreover, through the integration of moiré superlattices with silicon single-mode cavities, we find that the devices employing moiré-trapped IXs exhibit a significantly
lower threshold, one order of magnitude smaller compared to the device utilizing delocalized IXs. These findings not only encourage the exploration of many-body physics in moiré
superlattices at elevated temperatures but also pave the way for leveraging these artificial quantum materials in photonic and optoelectronic applications.
October 2024.
On-demand heralded MIR single-photon source using a cascaded quantum system
Jake Iles-Smith, Mark Kamper Svendsen, Angel Rubio, Martijn Wubs, Nicolas Stenger
submitted |
ArXiv:2405.12777
| view abstract
Abstract: We propose a novel mechanism for generating single photons in the mid-Infrared (MIR) using a solid-state or molecular quantum emitter.
The scheme utilises cavity QED effects to selectively enhance a Frank-Condon transition, deterministically preparing a single Fock state of a polar phonon mode.
By coupling the phonon mode to an antenna, the resulting excitation is then radiated to the far field as a single photon with a frequency matching the phonon mode.
By combining macroscopic QED calculations with methods from open quantum system theory, we show that optimal parameters to generate these MIR photons occur for
modest light-matter coupling strengths, which are achievable with state-of-the-art technologies. Combined, the cascaded system we propose provides a new quasi-deterministic
source of heralded single photons in a regime of the electromagnetic spectrum where this previously was not possible.
May 2024.
Omnidirectional gradient force optical trapping in dielectric nanocavities by inverse design
B. Martinez de Aguirre Jokisch, B. F. Gøtzsche, P. T. Kristensen, M. Wubs, O. Sigmund, and R. E. Christiansen
ACS Photonics, in press (2024)
|
ArXiv:2404.15102
| view abstract
Abstract: Optical trapping enables precise control of individual particles of different sizes, such as atoms, molecules, or nanospheres. Optical tweezers
provide free-space omnidirectional optical trapping of objects in laboratories around the world. As an alternative to standard macroscopic setups based on lenses,
which are inherently bound by the diffraction limit, plasmonic and photonic nanostructures promise trapping by near-field optical effects on the extreme nanoscale.
However, the practical design of lossless waveguide-coupled nanostructures capable of trapping deeply sub-wavelength particles in all spatial directions using the
gradient force has until now proven insurmountable. In this work, we demonstrate an omnidirectional optical trap realized by inverse-designing fabrication-ready
integrated dielectric nanocavities. The sub-wavelength optical trap is designed to rely solely on the gradient force and is thus particle-size agnostic. In particular,
we show how a nanometer-sized trapped particle experiences a force strong enough to overcome room-temperature thermal fluctuations. Furthermore, through the robust
inverse design framework, we tailor manufacturable devices operating at near-infrared and optical frequencies. Our results open a new regime of levitated optical trapping
by achieving a deep trapping potential capable of trapping single sub-wavelength particles in all directions using optical gradient forces. We anticipate potentially
groundbreaking applications of the optimized optical trapping system for biomolecular analysis in aqueous environments, levitated cavity-optomechanics, and cold atom physics,
constituting an important step towards realizing integrated bio-nanophotonics and mesoscopic quantum mechanical experiments.
April 2024.
Full quantitative near-field characterization of strongly coupled exciton-plasmon polaritons in thin-layered WSe2 on a monocrystalline gold platelet
Laura N. Casses, Binbin Zhou, Qiaoling Lin, Annie Tan, Diane-Pernille Bendixen-Fernex de Mongex, Korbinian J. Kaltenecker, Sanshui Xiao, Martijn Wubs, Nicolas Stenger
ACS Photonics 11, 3593 (2024) (open access)
|
ArXiv:2403.18655
| view abstract
Abstract: Exciton-plasmon polaritons (EPPs) are attractive both for the exploration of fundamental phenomena and
applications in nanophotonics. Previous studies of EPPs mainly relied on far-field characterization. Here, using near-field optical microscopy,
we quantitatively characterize the dispersion of EPPs existing in 13-nm-thick tungsten diselenide (WSe2) deposited on a monocrystalline gold platelet.
We extract from our experimental data a Rabi splitting of 81 meV, and an experimental effective polariton loss of 55 meV, demonstrating that our system
is in the strong-coupling regime. Furthermore, we measure for the first time at visible wavelengths the propagation length of these EPPs for each excitation
energy of the dispersion relation. To demonstrate the quantitative nature of our near-field method to obtain the full complex-valued wavevector of EPPs, we use
our near-field measurements to predict, via the transfer matrix method, the far-field reflectivities across the exciton resonance. These predictions are in excellent
agreement with our experimental far-field measurements. Our findings open the door towards the full near-field study of light-manipulating devices at the nanoscale.
March 2024.
News & Views: Multiphoton quantum statistics from scattered classical light
Martijn Wubs
Nature Physics 20, 689 (2024)
|
Open access version
| view abstract
| See also
M. Hong et al., Nat. Phys. (2024).
Abstract: Even by shining classical light on a single opening, one can perform a double-slit experiment and discover a
surprising variety of quantum mechanical multi-photon correlations — thanks to surface plasmon polaritons and photon-number-resolving detectors.
March 2024.
Collective photon emission in solid state environments:
Concatenating non-markovian and markovian dynamics
Devashish Pandey and Martijn Wubs
Phys. Rev. Res. 6, 033044 (2024) (Open Access)
| download pdf
|
ArXiv:2311.04741
| view abstract
Abstract: Collective light emission and multiqubit dynamics of solid-state quantum emitters are affected both by their coupling to the light field
and to lattice vibrations. The effect of phonons on quantum emitters is twofold: polaron formation is described by ultrafast non-Markovian dynamics, while
slower dephasing is well described by exponential decay. Of the two temperature-dependent processes, the effect of the former on the collective emission and
the entanglement decay of emitters is usually not modeled, and also the latter is sometimes neglected. Here we propose and compare two methods that are efficient
also for several emitters: the first method concatenates the fast and slow phonon dynamics, and the second is the polaron method. For a single quantum emitter, we
show that the dynamical equations are identical in both methods, while predictions for two or more emitters also agree very well. Both of our methods incorporate
non-Markovian dynamics due to phonons demonstrating the temperature sensitivity of the collective photon emission. Utilizing a simplified Markovian model instead
may not be accurate enough especially for quantum information applications: for example, we show how the Markovian model may considerably overestimate the two-emitter
concurrence, except at very low temperatures. Our concatenation and polaron methods can be applied to an arbitrary number and type of quantum emitters, and beyond the
bulk GaAs environment that we consider here. Especially the concatenation method can take phonon effects into account at the same computational cost as modeling the
emitter-photon interaction alone. Finally, we present approximate analytical expressions for the collective emission spectrum for 𝑁 emitters on a one-dimensional chain.
November 2023.
Observation of multiple bulk bound states in the continuum modes in a photonic crystal cavity
R. Chen, Y. Zheng, X. Huang, Q. Lin, C. Ye, M. Xiong, M. Wubs, Y. Ma, M. Pu, and S. Xiao
Beilstein J. Nanotechnol. 14, 544 (2023)
| download pdf
| view abstract
Abstract: Obtaining bound states in the continuum (BICs) in photonic crystals gives rise to the realization of resonances with high quality
factors for lasing and nonlinear applications. For BIC cavities in finite-size photonic crystals, the bulk resonance band turns into
discrete modes with different mode profiles and radiation patterns. Here, photonic-crystal BIC cavities encircled by the photonic
bandgap of lateral heterostructures are designed. The mirror-like photonic bandgap exhibits strong side leakage suppression to
confine the mode profile in the designed cavity. Multiple bulk quantized modes are observed both in simulation and experiment.
After exciting the BIC cavity at different positions, different resonance peaks are observed. The physical origin of the dependence
between the resonance peak and the illuminating position is explained by analyzing the mode profile distribution and further verified
by numerical simulations. Our findings have potential applications regarding the mode selectivity in BIC devices to manipulate
the lasing mode in photonic-crystal surface-emitting lasers or the radiation pattern in nonlinear optics.
April 2023.
A room-temperature moiré interlayer exciton laser
Q. Lin, H. Fang, Y. Liu, Y. Zhang, M. Fischer, J. Li, J. Hagel, S. Brem, E. Malic, N. Stenger, Z. Sun, M. Wubs, and S. Xiao
submitted
|
ArXiv:2302.01266
| view abstract
Abstract: Moiré superlattices in van der Waals heterostructures offer highly tunable quantum systems with emergent electronic and
excitonic properties such as superconductivity, topological edge states, and moiré-trapped excitons. Theoretical calculations predicted the existence of
the moiré potential at elevated temperatures; however, its impact on the optical properties of interlayer excitons (IXs) at room temperature is lacking,
and the benefits of the moiré effects for lasing applications remain unexplored. We report that the moiré potential in a molybdenum disulfide/tungsten
diselenide (MoS2/WSe2) heterobilayer system can significantly enhance light emission, elongate the IX lifetime, and modulate the IX emission energy at
room temperature. By integrating a moiré superlattice with a silicon topological nanocavity, we achieve ultra-low-threshold lasing at the technologically
important telecommunication O-band thanks to the significant moiré modulation. Moreover, the high-quality topological nanocavities facilitate the highest
spectral coherence of < 0.1 nm linewidth among all reported two-dimensional material-based laser systems. Our findings not only open a new avenue for
studying correlated states at elevated temperatures, but also enable novel architectures for integrated on-chip photonics and optoelectronics.
February 2023.
Quantum optical effective-medium theory for layered metamaterials at any angle of incidence
Ehsan Amooghorban and Martijn Wubs
Nanomaterials 13, 291 (2023) (Open Access)
| download pdf
|
ArXiv:1606.07912
| view abstract
Abstract: The quantum optics of metamaterials starts with the question whether the same effective-medium theories apply as in classical optics.
In general the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter
is indispensable besides the effective index, namely the effective noise-photon distribution. Only with the extra parameter can one predict how well
the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one
additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here from a Lagrangian
description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light
propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work [ E. Amooghorban et al.,
Phys. Rev. Lett. 110, 153602 (2013)]. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories.
As our main result we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization
and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a
thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate
predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.
December 2022.
Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin
M. Fischer, A. Sajid, J. Iles-Smith, A. Hötger, D. I. Miakota, M. K. Svendsen, C. Kastl, S. Canulescu, S. Xiao, M. Wubs, K. S. Thygesen, A. W. Holleitner and N. Stenger
Nanoscale 15, 14215 (2023) (open access)
| download pdf
| ArXiv:2209.08910 |
view abstract
Abstract: The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies around 2 eV which
exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with
non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line
shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed
enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves
higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism
with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and
will help to identify their microscopic origin.
September 2022.
Graphene multilayers for coherent perfect absorption: effects of interlayer separation
Devashish Pandey, Sanshui Xiao, Martijn Wubs
Opt. Express 30, 44504 (2022)
| download pdf
|
ArXiv:2209.02023 |
view abstract |
Abstract: We present a model study to estimate the sensitivity of the optical absorption
of multilayered graphene structure to the subnanometer interlayer separation. Starting
from a transfer-matrix formalism we derive semi-analytical expressions for the far-field
observables. Neglecting the interlayer separation, results in upper bounds to the absorption
of fifty percent for real-valued sheet conductivities, exactly the value needed for coherent
perfect absorption (CPA), while for complex-valued conductivities we identify upper bounds
that are always lower. For pristine graphene the number of layers required to attain this maximum
is found to be fixed by the fine structure constant. For finite interlayer separations we find that
this upper bound of absorption only exists until a particular value of interlayer separation which
is less than the realistic interlayer separation in graphene multilayers. Beyond this value, we find
a strong dependence of absorption with the interlayer separation. For an infinite number of graphene
layers a closed-form analytical expression for the absorption is derived, based on a continued-fraction
analysis. Our comparison with experiments illustrates that multilayer Van der Waals crystals suitable
for CPA can be more accurately modelled as electronically independent layers and more reliable predictions
of their optical properties can be obtained if their subnanometer interlayer separations are carefully accounted for.
September 2022.
Spectral tuning, stabilities under external exposures, and spontaneous enhancement of
emission intensity in grown-into-glass all-inorganic metal halide perovskite nanocrystals
F. Kang, Y. Du, Z. Yang, P. Boutinaud, M. Wubs, Jie Xu, H. Ou, D. Li, K. Zheng, A.T. Tarekegne, G. Sun, X. Xu, and S. Xiao
Laser & Photonics Reviews 16, 2200166 (2022)
| download pdf
|
view abstract |
Abstract: (Abstract coming soon)
August 2022.
Fabry-Perot microcavity spectra have a fine structure
M. P. van Exter, M. Wubs, E. Hissink, C. Koks
Phys. Rev. A 106, 013501 (2022)
| download pdf
| ArXiv:2203.01638
|
view abstract | see also:
Observation of microcavity fine structure
Abstract: Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance
frequencies of these modes cluster in different orders. A non-paraxial vector theory predicts that the frequency degeneracy within these clusters
is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper,
we calculate this fine structure for microcavities and show how it originates from various non-paraxial effects and is co-determined by mirror
aberrations. The presented theory, which applies perturbation theory to Maxwell's equations with boundary conditions, proves to be very powerful.
It generalizes the effective 1-dimensional description of Fabry-Perot cavities to a 3-dimensional multi-transverse-mode description. It thereby
provides new physical insights in several mode-shaping effects and a detailed prediction of the fine structure in Fabry-Perot spectra.
March 2022.
Quantitative near-field characterization of surface plasmon polaritons on monocrystalline gold platelets
Laura N. Casses, Korbinian J. Kaltenecker, Sanshui Xiao, Martijn Wubs, Nicolas Stenger
Opt. Express 30, 11181 (2022)
| download pdf
| ArXiv:2201.08725
|
view abstract
Abstract: The subwavelength confinement of surface plasmon polaritons (SPPs) makes them attractive for various applications
such as sensing, light generation and solar energy conversion. Near-field microscopy associated with interferometric detection allows to
visualize both the amplitude and phase of SPPs. However, their full quantitative characterization in a reflection configuration is
challenging due to complex wave patterns arising from the interference between several excitation channels. Here, we present near-field
measurements of SPPs on large monocrystalline gold platelets in the visible spectral range. We study systematically the influence of the
incident angle of the exciting light on the SPPs launched by an atomic force microscope tip. We find that the amplitude and phase signals
of these SPPs are best disentangled from other signals at grazing incident angle relative to the edge of the gold platelet. Furthermore,
we introduce a simple model to explain the phase shift observed between the SPP amplitude and phase profiles. Using this model, the wavelength
and propagation length of the tip-launched plasmons are retrieved by isolating and fitting their signals far from the platelets edges. Our
experimental results are in excellent agreement with theoretical models using gold refractive index values. The presented method to fully
characterize the SPP complex wavevector could enable the quantitative analysis of polaritons occurring in different materials at visible wavelengths.
January 2022.
Quantifying the breakdown of the rotating-wave approximation in single-photon superradiance
Mads Anders Jørgensen and Martijn Wubs
J. Phys. B: At. Mol. Opt. Phys. 55, 195401 (2022)
| download pdf
| ArXiv:2112.04952
|
view abstract
Abstract: We study quantitatively the breakdown of the rotating-wave approximation when calculating collective
light emission by quantum emitters, in particular in the weak-excitation limit. Our starting point is a known multiple-scattering
formalism where the full light-matter interaction leads to induced inter-emitter interactions described by the classical Green
function of inhomogeneous dielectric media. When making the RWA in the light-matter interaction, however, these induced interactions
differ from the classical Green function, and for free space we find a reduction of the interatomic interaction strength by up to a
factor of two. By contrast, for the corresponding scalar model the relative RWA error for the inter-emitter interaction even diverges
in the near field. For two identical emitters, the errors due to the RWA in collective light emission will show up in the emission
spectrum, but not in the sub- and superradiant decay rates. In case of two non-identical emitters, also the collective emission rates
will differ by making the RWA. For three or more identical emitters, the RWA errors in the interatomic interaction in general affect both
the collective emission spectra and the collective decay rates. Ring configurations with discrete rotational symmetry are an interesting
exception. Interestingly, the maximal errors in the collective decay rates due to making the RWA do not occur in the extreme near-field limit.
December 2021.
Strongly direction-dependent magnetoplasmons in mixed Faraday-Voigt configurations
Afshin Moradi and Martijn Wubs
Sci. Rep. 11, 18373 (2021)
| download pdf
| ArXiv:2105.09147
|
view abstract
Abstract: The electrostatic theory of magnetoplasmons on a semi-infinite magnetized electron gas is generalized to mixed
Faraday-Voigt configurations. We analyze a new type of electrostatic surface waves that is strongly direction-dependent, and may be realized
on narrow-gap semiconductors in the THz regime. A general expression for the dispersion relation is presented, with its dependence on the
magnitude and orientation of the applied magnetic field. Remarkably, the group velocity is always perpendicular to the phase velocity. Both
velocity and energy relations of the found magnetoplasmons are discussed in detail. In the appropriate limits the known magnetoplasmons in the
higher-symmetry Faraday and Voigt configurations are recovered.
May 2021.
Quantum theory of two-dimensional materials coupled to electromagnetic resonators
E. V. Denning, M. Wubs, N. Stenger, J. Mork, P. T. Kristensen
Phys. Rev. B 105, 085306 (2022)
| download pdf
| ArXiv:2103.14488
|
view abstract
Abstract: We present a microscopic quantum theory of light-matter interaction in pristine sheets of two-dimensional semiconductors coupled to
localized electromagnetic resonators such as optical nanocavities or plasmonic particles. The light-matter interaction breaks the translation symmetry of excitons
in the two-dimensional lattice, and we find that this symmetry-breaking interaction leads to the formation of a localized exciton state, which mimics the spatial
distribution of the electromagnetic field of the resonator. The localized exciton state is in turn coupled to an environment of residual exciton states. We quantify the
influence of the environment and find that it is most pronounced for small lateral confinement length scales of the electromagnetic field in the resonator, and that
environmental effects can be neglected if this length scale is sufficiently large. The microscopic theory provides a physically appealing derivation of the coupled-oscillator
models widely used to model experiments on these types of systems, in which all observable quantities are directly derived from the material parameters and the properties of
the resonant electromagnetic field. As a consistency check, we show that the theory recovers the results of semiclassical electromagnetic calculations and experimental
measurements of the excitonic dielectric response in the linear excitation limit. The theory, however, is not limited to linear response, and in general describes nonlinear
exciton-exciton interactions in the localized exciton state, thereby providing a powerful means of investigating the nonlinear optical response of such systems.
March 2021.
Cavity-induced exciton localisation and polariton blockade in two-dimensional semiconductors coupled to an electromagnetic resonator
E. V. Denning, M. Wubs, N. Stenger, J. Mork, P. T. Kristensen
Phys. Rev. Research 4, L012020 (2022) (open access)
| download pdf
| ArXiv:2103.14484
|
view abstract
Abstract: Recent experiments have demonstrated strong light–matter coupling between electromagnetic nanoresonators and pristine sheets of two-dimensional
semiconductors, and it has been speculated whether these systems can enter the quantum regime operating at the few-polariton level. To address this question, we
present a microscopic quantum theory for the interaction between excitons in a sheet of two-dimensional material and a localized electromagnetic resonator. We find that the
light–matter interaction breaks the symmetry of the otherwise translation-invariant system and thereby effectively generates a localized exciton mode, which is coupled to an
environment of residual exciton modes. This dissipative coupling increases with tighter lateral confinement, and our analysis reveals this to be a potential challenge in
realizing nonlinear exciton-exciton interaction. Nonetheless, we predict that polariton blockade due to nonlinear exciton-exciton interactions is well within reach for
nanoresonators coupled to transition-metal dichalcogenides, provided that the lateral confinement can be sufficiently tight to make the nonlinearity overcome the polariton
dephasing caused by phonon interactions.
March 2021.
Controlled Generation of Luminescent Centres in Hexagonal Boron Nitride by Irradiation Engineering
M. Fischer, J. M. Caridad, A. Sajid, S. Ghaderzadeh, M. Ghorbani-Asl, L. Gammelgaard, P.
Bøggild, K. S. Thygesen, A. V. Krasheninnikov, S. Xiao, M. Wubs, and N. Stenger
Sci. Adv. 7, eabe7138 (2021)
| download pdf
|
view abstract
Abstract: Luminescent centers in the two-dimensional material hexagonal boron nitride have the potential to enable quantum
applications at room temperature. To be used for applications, it is crucial to generate these centers in a controlled
manner and to identify their microscopic nature. Here, we present a method inspired by irradiation engineering
with oxygen atoms. We systematically explore the influence of the kinetic energy and the irradiation fluence on
the generation of luminescent centers. We find modifications of their density for both parameters, while a fivefold
enhancement is observed with increasing fluence. Molecular dynamics simulations clarify the generation mechanism
of these centers and their microscopic nature. We infer that V_{N}C_{B} and V_{B}^{−} are the most likely centers formed. Ab
initio calculations of their optical properties show excellent agreement with our experiments. Our methodology
generates quantum emitters in a controlled manner and provides insights into their microscopic nature.
February 2021.
Quantum Langevin approach for superradiant nanolasers
Igor Protsenko, Alexander Uskov, Emil Cortes André, Jesper Mork, and Martijn Wubs
New J. Phys. 23, 063010 (2021) | ArXiv:2012.02533
| download pdf
|
view abstract
Abstract: A new approach for analytically solving quantum nonlinear Langevin equations is proposed and
applied to calculations of spectra of superradiant lasers where collective effects play an important
role. We calculate lasing spectra for arbitrary pump rates and recover well-known results such as
the pump dependence of the laser linewidth across the threshold region. We predict new sideband
peaks in the spectrum of superradiant lasers with large relaxation oscillations as well as new nonlinear
structures in the lasing spectra for weak pump rates. Our approach sheds new light on the
importance of population fluctuations in the narrowing of the laser linewidth, in the structure of
the lasing spectrum, and in the transition to coherent operation.
December 2020.
Efficient stochastic simulation of rate equations and photon statistics of nanolasers
Emil Cortes André, Jesper Mork, Martijn Wubs
Opt. Express 28, 32632 (2020)
| download pdf
| ArXiv:2008.11456 |
view abstract
Abstract: Based on a rate equation model for single-mode two-level lasers, two algorithms for stochastically simulating the dynamics
and steady-state behaviour of micro- and nanolasers are described in detail. Both methods lead to steady-state photon numbers and
statistics characteristic of lasers, but one of the algorithms is shown to be significantly more efficient. This algorithm, known
as Gillespie's First Reaction Method (FRM), gives up to a thousandfold reduction in computation time compared to earlier algorithms,
while also circumventing numerical issues regarding time-increment size and ordering of events. The FRM is used to examine
intra-cavity photon distributions, and it is found that the numerical results follow the analytics exactly. Finally, the FRM is
applied to a set of slightly altered rate equations, and it is shown that both the analytical and numerical results exhibit
features that are typically associated with the presence of strong inter-emitter correlations in nanolasers.
August 2020.
Plasmonic semiconductor nanoparticles showing nonlocal response
Tahereh Golestanizadeh, Klaas-Jan Gorter, Johan R. Maack, and Martijn Wubs
J. Phys.: Conf. Ser. 1537, 012001 (2020) (open access)
| download pdf |
view abstract
Abstract: We predict that localized surface plasmons (LSP) in semiconductor particles exhibit
spatial nonlocal response effects as the geometry enters the nanometer scale. To investigate these
nonlocal effects, we first apply the hydrodynamic model (HDM) to nanospheres of two different
semiconductor materials: intrinsic InSb and n-doped GaAs. Our results show that the
semiconductors indeed display nonlocal effects, and that these effects are even more pronounced
than in metals, and more tunable as well. We also present a two-fluid hydrodynamic model for
semiconductors containing electrons and holes (from thermal or external excitation) or light and
heavy holes (in p-doped materials). The two-fluid model predicts the existence of two
longitudinal modes, an acoustic and an optical, whereas only an optical mode is present in the
HDM. By extending nonlocal Mie theory to two plasmas, we simulate the optical properties of
two-fluid nanospheres and predict that the acoustic mode gives rise to peaks in the extinction
spectra that are absent in the HDM. And from a numerical study, we predict that by considering
dimers rather than monomers of nanowires, the extinction cross section and field enhancement
of the acoustic localized surface plasmon resonances can increase substantially. In this
conference proceedings, we present calculations of the two-fluid GNOR model, which show that
acoustic surface plasmon modes are surprisingly robust against size-dependent broadening.
June 2020.
Ultra-subwavelength focusing and giant magnetic-field enhancement in a low-loss one-way waveguide based on remanence
Jie Xu, Xiaohua Deng, Hang Zhang, Chiaho Wu, Martijn Wubs, Sanshui Xiao, Linfang Shen
J. Opt. 22, 025003 (2020)
| download pdf |
ArXiv:1909.07848 |
view abstract
Abstract: The subwavelength focusing based on surface plasmon polaritons (SPP) has been widely explored in tapered metallic structures. However, the efficiency of
energy localization is relatively weak, largely due to high propagation loss and strong back reflection. Here, we propose a straight-tapered 3-dimensional (3D) one-way surface
magnetoplasmon (SMP) waveguide with the ending surface of a hundred million times smaller than the squared wavelength, to achieve energy focusing in the microwave regime. Due to low propagation
loss of SMP, we achieve huge magnetic field enhancement in such an ultra-subwavelength area, by five orders of magnitude. Instead of using an external static magnetic field, our proposed
SMP waveguide relies on remanence, which is very convenient for operating practical 3D applications. These results show promising applications in magnetic-field enhancing or quenching
fluorescence, luminescence or nonlinearity of 2D materials, novel scanning near-field microwave microscopy and energy storage.
September 2019.
Preparing pure states with lossy beam splitters using quantum coherent absorption of squeezed light
Martijn Wubs and Ali Ü. C. Hardal
Proc. SPIE 11091 Quantum Nanophotonic Materials, Devices, and Systems, 110910Z (2019)
|
view abstract
Abstract: We investigate coherent perfect absorption (CPA) of squeezed coherent states of light by an absorbing beam splitter. First we derive the absorption coefficients for
quantum coherence and for intensity, which generally differ. Secondly, we present the remarkable properties of a CPA-gate: two identical but otherwise arbitrary incoming squeezed
coherent states can be completely stripped off their coherence, producing a pure entangled squeezed vacuum state at the output. Importantly, this output state of light is not entangled
with the absorbing beam splitter by which it was produced. This makes the CPA gate potentially interesting for continuous-variable quantum state preparation.
September 2019.
Hydrodynamic acoustic plasmon resonances in semiconductor nanowires and their dimers
Tahereh Golestanizadeh, Abbas Zarifi, Tahmineh Jalali, Johan R. Maack, and Martijn Wubs
JOSA B 36, 2712 (2019)
|
download pdf |
ArXiv:1905.10642 |
view abstract
Abstract: The hydrodynamic Drude model known from metal plasmonics also applies to semiconductor structures of sizes in between
single-particle quantum confinement and bulk. But contrary to metals, for semiconductors two or more types of plasma may have to be taken
into account in order to properly describe their plasmonic properties. In this combined analytical and computational study, we explore
predictions of the recently proposed two-fluid hydrodynamic Drude model for the optical properties of plasmonic semiconductor nanowires,
in particular for thermally excited InSb nanowires. We focus on the low-frequency acoustic surface and bulk plasmon resonances that are unique
fingerprints for this model and are yet to be observed. We identify these resonances in spectra for single nanowires based on analytical calculations,
and they are in complete agreement with our numerical implementation of the model. For dimers of nanowires we predict substantial increase of the extinction
cross section and field enhancement of the acoustic localized surface plasmon resonance, which makes its observation in dimers more likely.
May 2019.
Single-Crystalline Gold Nanodisks on WS2 Mono- and Multilayers for Strong Coupling at Room Temperature
Mathias Geisler, Ximin Cui, Jianfang Wang, Tomas Rindzevicius, Lene Gammelgaard, Bjarke S. Jessen, P. A. D. Gonçalves,
Francesco Todisco, Peter Bøggild, Anja Boisen, Martijn Wubs, N. Asger Mortensen, Sanshui Xiao, Nicolas Stenger
ACS Photonics 6, 994 (2019)
|
download pdf |
ArXiv:1812.09495 |
view abstract
Abstract: Engineering light-matter interactions up to the strong-coupling regime at room temperature is one of the cornerstones of modern nanophotonics.
Achieving this goal will enable new platforms for potential applications such as quantum information processing, quantum light sources and
even quantum metrology. Materials like transition metal dichalcogenides (TMDC) and in particular tungsten disulfide (WS2) possess large transition
dipole moments comparable to semiconductor-based quantum dots, and strong exciton binding energies allowing the detailed exploration of light-matter
interactions at room temperature. Additionally, recent works have shown that coupling TMDCs to plasmonic nanocavities with light tightly focused on
the nanometer scale can reach the strong-coupling regime at ambient conditions. Here, we use ultra-thin single-crystalline gold nanodisks featuring
large in-plane electromagnetic dipole moments aligned with the exciton transition-dipole moments located in monolayer WS2. Through scattering and
reflection spectroscopy we demonstrate strong coupling at room temperature with a Rabi splitting of 108 meV. In order to go further into the
strong-coupling regime and inspired by recent experimental work by Stührenberg et al., we couple these nanodisks to multilayer WS2. Due to an increase
in the number of excitons coupled to our nanodisks, we achieve a Rabi splitting of 175 meV, a major increase of 62 percent. To our knowledge, this is the
highest Rabi splitting reported for TMDCs coupled to open plasmonic cavities. Our results suggest that ultra-thin single-crystalline gold nanodisks
coupled to WS2 represent an exquisite platform to explore light-matter interactions.
December 2018.
Magnetoplasmons in monolayer black phosphorus structures
Y. You, P. A. D. Gonçalves, L. Shen, M. Wubs, X. Deng, and S. Xiao
Opt. Lett. 44, 554 (2019)
|
download pdf |
ArXiv:1910.14577 |
view abstract
Abstract: Two-dimensional materials supporting deep subwavelength plasmonic modes can also exhibit
strong magneto-optical responses. Here, we theoretically investigate magnetoplasmons in monolayer black
phosphorus structures under moderate static magnetic fields. We consider three different structures, namely,
a continuous black phosphorus monolayer, an edge formed by a semi-infinite sheet, and finally a triangular
wedge configuration. Each of these structures show strongly anisotropic magneto-optical responses
induced both by the external magnetic field and by the intrinsic anisotropy of the black phosphorus lattice.
Starting from the magneto-optical conductivity of a single-layer of black phosphorus, we derive the dispersion
relation of the ensuing magnetoplasmons in the considered geometries, using a combination of analytical,
semi-analytical, and numerical methods. We fully characterize the magnetoplasmons’ dispersions and the
properties of the corresponding field distributions, and show that these structures sustain strongly anisotropic
subwavelength modes that are highly tunable. Our results demonstrate that magnetoplasmons in monolayer
black phosphorus, with its inherent lattice anisotropy as well as magnetically-induced anisotropy, hold
potential for tunable anisotropic materials operating below the diffraction limit thereby paving the way for
tailored nanophotonic devices at the nanoscale.
October 2018.
On collective Rabi splitting in nanolasers and nano-LEDs
Emil C. André, Igor E. Protsenko, Alexander V. Uskov, Jesper Mork, Martijn Wubs
Opt. Lett. 44, 1415 (2019)
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download pdf |
ArXiv:1810.06098 |
view abstract
Abstract: We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many
incoherently pumped two-level emitters in a cavity. At low pump rates, we find two peaks in the spectrum for large coupling
strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and
discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will
never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible, we
show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems,
and discuss the influence of inter-emitter correlations on the lineshape.
October 2018.
Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons
Kåre Obel Wedel, N. Asger Mortensen, Kristian S. Thygesen, Martijn Wubs
Phys. Rev. B 99, 045411 (2019), selected for PRB's Kaleidoscope
| download pdf |
ArXiv:1809.09952 |
view abstract
Abstract: We investigate higher-order plasmons in graphene nanoribbons, and present how electronic edge states and wavefunction fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wavefunction oscillations induced by inter-valley coupling. Interestingly, the wavefunction fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.
September 2018.
Emergent scale invariance of non-classical plasmons in graphene nanoribbons
Kåre Obel Wedel, N. Asger Mortensen, Kristian S. Thygesen, Martijn Wubs
Phys. Rev. B 98, 155412 (2018)
| download pdf |
ArXiv:1807.04552 |
view abstract
Abstract: Using a nearest-neighbor tight-binding model we investigate quantum effects of plasmons on few-nanometer wide graphene nanoribbons, both for zigzag and armchair edge terminations. With insight from the Dirac description we find an emerging scale-invariant behavior that deviates from the classical model both for zigzag and armchair structures. The onset of the deviation can be related to the position of the lowest parabolic band in the band structure. Dirac theory is only valid in the parameter subspace where the scale invariance holds that relates narrow ribbons with high doping to wide ribbons with low doping. We also find that the edge states present in zigzag ribbons give rise to a blueshift of the plasmon, in contrast to earlier findings for graphene nanodisks and nanotriangles.
July 2018.
Quantum coherent absorption of squeezed light
Ali Ü. C. Hardal, Martijn Wubs
Optica 6, 181 (2019)
| download pdf |
ArXiv:1805.02884 |
view abstract
Abstract: We investigate coherent perfect absorption (CPA) in quantum optics, in particular when pairs of squeezed coherent states of light are superposed on an absorbing beam splitter.
First, by employing quantum optical input-output relations, we derive the absorption coefficients for quantum coherence and for intensity, and reveal how these will differ for squeezed states.
Secondly, we present the remarkable properties of a CPA-gate for continuous-variable quantum state preparation: two identical but otherwise arbitrary incoming squeezed coherent states can be completely
stripped of their coherence, producing a pure entangled squeezed vacuum state that with its finite intensity escapes from an otherwise perfect absorber. Importantly, this output state of light is not
entangled with the absorbing beam splitter by which it was produced.
May 2018.
Two-fluid hydrodynamic model for semiconductors
Johan R. Maack, N. Asger Mortensen, Martijn Wubs
Phys. Rev. B 97, 115415 (2018) |
download pdf |
ArXiv:1712.08580 |
view abstract
Abstract: The hydrodynamic Drude model (HDM) has been successful in describing the optical properties of
metallic nanostructures, but for semiconductors where several different kinds of
charge carriers are present, an extended theory is required. We present a two-fluid
hydrodynamic model for semiconductors containing electrons and holes (from thermal
or external excitation) or light and heavy holes (in p-doped materials). The
two-fluid model predicts the existence of two longitudinal modes, an acoustic and
an optical, whereas only an optical mode is present in the HDM. By extending
nonlocal Mie theory to two plasmas, we are able to simulate the optical properties
of two-fluid nanospheres and predict that the acoustic mode gives rise to peaks in
the extinction spectra that are absent in the HDM.
Dec. 2017.
Collective effects in nanolasers explained by generalized rate equations
Igor Protsenko, Emil C. André, Alexander Uskov, Jesper Mørk, and Martijn Wubs
submitted |
ArXiv:1709.08200 |
view abstract
Abstract: We study the stationary photon output and statistics of small lasers. Our closed-form expressions clarify the contribution of collective effects due to the interaction between quantum emitters. We generalize laser rate equations and explain photon trapping: a decrease of the photon number output below the lasing threshold, derive an expression for the stationary cavity mode autocorrelation function $g_2$, which implies that collective effects may strongly influence the photon statistics. We identify conditions for coherent, thermal and superthermal radiation, the latter being a unique fingerprint for collective emission in lasers. These generic analytical results agree with recent experiments, complement numerical results, and provide insight into and design rules for nanolasers.
Sept. 2017.
Robustness of the Rabi splitting under nonlocal corrections in plexcitonics
Christos Tserkezis, Martijn Wubs, and N. Asger Mortensen
ACS Photonics 5, 133 (2018) |
download pdf |
ArXiv:1707.05134 |
view abstract
Abstract: We explore theoretically how nonlocal corrections in the description of the metal affect the strong coupling between excitons and plasmons in typical examples where nonlocal effects are anticipated to be strong, namely small metallic nanoparticles, thin metallic nanoshells or dimers with narrow separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalised nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations, the influence of nonlocality is rather limited, as in most occasions the width of the Rabi splitting remains largely unaffected and the two hybrid modes are well distinguishable. We discuss how this behaviour can be understood in view of the popular coupled-harmonic-oscillator model, while we also provide analytic solutions based on Mie theory to describe the hybrid modes in the case of matryoshka-like single nanoparticles. Our analysis provides an answer to a so far open question, that of the influence of nonlocality on strong coupling, and is expected to facilitate the design and study of plexcitonic architectures with ultrafine geometrical details.
July 2017.
Size-dependent nonlocal effects in plasmonic semiconductor particles
J. R. Maack, N. A. Mortensen, and M. Wubs
EPL 119, 17003 (2017) |
download pdf |
ArXiv:1706.03813 |
view abstract
Abstract: Localized surface plasmons (LSP) in semiconductor particles are expected to exhibit spatial nonlocal response effects as the geometry enters the nanometer scale. To investigate these nonlocal effects, we apply the hydrodynamic model to nanospheres of two different semiconductor materials: intrinsic InSb and n-doped GaAs. Our results show that the semiconductors indeed display nonlocal effects, and that these effects are even more pronounced than in metals. In a 150 nm InSb particle at 300K, the LSP frequency is blueshifted 35 percent, which is orders of magnitude larger than the blueshift in a metal particle of the same size. This property, together with their tunability, makes semiconductors a promising platform for experiments in nonlocal effects.
June 2017.
How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps
Christos Tserkezis, N. Asger Mortensen, and Martijn Wubs
Phys. Rev. B 96, 085413 (2017) |
download pdf |
ArXiv:1703.00728 |
view abstract
Abstract: The nonclassical modification of plasmon-assisted fluorescence enhancement is theoretically explored by placing two-level dipole emitters at the narrow gaps encountered in canonical plasmonic architectures, namely dimers and trimers of different metallic nanoparticles. Through detailed simulations, in comparison with appropriate analytical modelling, it is shown that within classical electrodynamics, and for the reduced separations explored here, fluorescence enhancement factors of the order of a hundred thousand can be achieved, with a divergent behaviour as the particle touching regime is approached. This remarkable prediction is mainly governed by the dramatic increase in excitation rate triggered by the corresponding field enhancement inside the gaps. Nevertheless, once nonclassical corrections are included, the amplification factors decrease by up to two orders of magnitude and a saturation regime for narrower gaps is reached. These nonclassical limitations are demonstrated by simulations based on the generalised nonlocal optical response theory, which accounts in an efficient way not only for nonlocal screening, but also for the enhanced Landau damping near the metal surface. A simple strategy to introduce nonlocal corrections to the analytic solutions is also proposed. It is therefore shown that the nonlocal optical response of the metal imposes more realistic, finite upper bounds to the enhancement feasible with ultrasmall plasmonic cavities, thus providing a theoretical description closer to state of the art experiments.
March 2017.
On the origin of nonlocal damping in plasmonic monomers and dimers
C. Tserkezis, W. Hsieh, G. Sun, J. B. Khurgin, M. Wubs, and N. A. Mortensen
Int. J. of Modern Phys. B 31, 1740005 (2017) | download pdf |
view abstract
Abstract: The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with time-dependent density-functional-theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic architectures: metal-dielectric interfaces,
metal-dielectric-metal gaps, spherical nanoparticles, and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective-diffusive GNOR theory, describes
well the enhanced losses and plasmon broadening predicted by ab initio calculations in few-nm particles or few-to-sub-nm gaps. Through the evaluation of a local effective
dielectric function, it is shown that absorptive losses appear dominantly close to the metal surface, in agreement with TDDFT and the mechanism of Landau damping due to generation of electron-hole pairs at the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies.
March 2017.
Nonlocal Response in Plasmonic Nanostructures
Martijn Wubs and N. Asger Mortensen
Book chapter pp 279-302 in the book
Quantum Plasmonics (Springer, Cham, 2017), Volume 185 of the Springer Series in Solid-State Sciences, edited by S.I. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal
|
view abstract
Abstract: After a brief overview of nanoplasmonics experiments that defy explanation with classical electrodynamics, we introduce nonlocal response as a main reason for non-classical effects. This concept is first introduced phenomenologically, and afterwards based on the semi-classical hydrodynamic Drude model (HDM) that indeed exhibits nonlocal response. In particular, we discuss recent generalizations and extensions of the HDM, to include both convection and diffusion dynamics of the induced charges. This generalized nonlocal optical response (GNOR) model allows for the first time unified semi-classical explanations of known experimental phenomena for both monomers and dimers that previously seemed to require microscopic theory. Finally, we turn to Landau damping and discuss the microscopic origin of the size-dependent damping captured by the classical diffusion mechanism in the GNOR model.
November 2016.
A hybridizable discontinuous Galerkin method for solving nonlocal optical response models
Liang Li, Stéphane Lanteri, N. Asger Mortensen, and Martijn Wubs
Computer Phys. Commun. 219, 99 (2017) | download pdf |
ArXiv:1611.08313 |
view abstract
Abstract: We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed to describe the optical properties of nano-plasmonic scatterers and waveguides. Brief derivations for both the NHD model and the GNOR model are presented. The formulations of the HDG method are given, in which we introduce two hybrid variables living only on the skeleton of the mesh. The local field solutions are expressed in terms of the hybrid variables in each element. Two conservativity conditions are globally enforced to make the problem solvable and to guarantee the continuity of the tangential component of the electric field and the normal component of the current density. Numerical results show that the proposed HDG methods converge at optimal rate. We benchmark our implementation and demonstrate that the HDG method has the potential to solve complex nanophotonic problems.
November 2016.
Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects
Christos Tserkezis, Nikolaos Stefanou, Martijn Wubs, and N. Asger Mortensen
Nanoscale 8, 17532 (2016)
| download pdf |
view abstract
Abstract: Molecular spontaneous emission and fluorescence depend strongly on the emitter local environment. Plasmonic nanoparticles provide excellent templates for tailoring fluorophore emission, as
they exhibit a potential for both fluorescence enhancement and quenching, depending on emitter positioning in the nanoparticle vicinity. Here we explore the influence of hitherto disregarded nonclassical effects in the description of emitter-plasmon hybrids, focusing on the roles of metal nonlocal response and especially size-dependent plasmon damping. Through extensive modelling of metallic nanospheres and nanoshells coupled to dipole emitters, we show that within a purely classical description a remarkable fluorescence enhancement can be achieved. However, once departing from the local-response approximation, and particularly by implementing the recent generalised nonlocal optical response theory, which provides a more complete physical description combining electron convection and diffusion, we show that not only are fluorescence rates dramatically reduced as compared to the predictions of the local description and the common hydrodynamic Drude model, but the optimum emitter-nanoparticle distance is also strongly affected. In this respect, experimental measurements of fluorescence, the theoretical description of which requires a precise concurrent evaluation of far- and near-field properties of the system, constitute a novel, more sensitive probe for assessing the validity of state-of-the-art nonclassical
theories.
September 2016.
Quantum optical effective-medium theory for layered metamaterials
Ehsan Amooghorban and Martijn Wubs
submitted
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ArXiv:1606.07912
| view abstract
Abstract: The quantum optics of metamaterials starts with the question whether the same effective-medium theories apply as in classical optics. In general the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our recent work [ E. Amooghorban et al., Phys. Rev. Lett. 110, 153602 (2013)]. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for TE-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for TM-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.
June 2016.
Robustness of the far-field response of nonlocal plasmonic ensembles
Christos Tserkezis, Johan R. Maack, Zhaowei Liu, Martijn Wubs, N. Asger Mortensen
Sci. Rep. 6, 28441 (2016)
| download pdf |
ArXiv:1602.00874
| view abstract |
conf. abstract Metamaterials Crete 2016
Abstract: Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles (NPs) are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron NPs, and within the simple nonlocal Hydrodynamic Drude Model (HDM), both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality to a lesser extent when the homogeneous size-dependent broadening of individual NPs is taken into account, either through a local size-dependent damping (SDD) model or through the Generalized Nonlocal Optical Response (GNOR) theory. The role of ensemble averaging is further explored in realistic distributions of noble-metal NPs, as encountered in experiments, while an analytical expression to evaluate the importance of inhomogeneous broadening through measurable quantities is developed. Our findings are independent of the specific nonclassical theory used, thus providing important insight into a large range of experiments on nanoscale and quantum plasmonics.
February 2016.
Transformation quantum optics: Designing spontaneous emission using coordinate transformations
Jingjing Zhang, Martijn Wubs, Pavel Ginzburg, Gregory Wurtz, and Anatoly V. Zayats
J. Opt. 18, 044029 (2016)
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download pdf
| view abstract
Abstract: Spontaneous decay is a fundamental quantum property of emitters that can be controlled in a
material environment via modification of the local density of optical states (LDOS). Here we use
transformation optics methods in order to design required density of states and thus spontaneous
emission (SE) rate. Specifically, we show that the SE rate can be either enhanced or suppressed
using invisibility cloaks or gradient index lenses. Furthermore, the anisotropic material profile of
the cloak enables the directional control of SE. We also discuss how the practical issues, such as
dispersion and losses, affect the LDOS in complex materials. Tailoring SE properties using
transformation optics approach provides an innovative way for designing emission properties in
a complex material environment needed for the development of active nanophotonic devices.
November 2015.
Classification of scalar and dyadic nonlocal optical response models
Martijn Wubs
Opt. Express 23, 31296 (2015)
| download pdf |
view abstract
Abstract: Nonlocal optical response is one of the emerging effects on the
nanoscale for particles made of metals or doped semiconductors. Here we classify
and compare both scalar and tensorial nonlocal response models. In the
latter case the nonlocality can stem from either the longitudinal response,
the transverse response, or both. In phenomenological scalar models
the nonlocal response is described as a smearing out of the commonly
assumed infinitely localized response, as characterized by a distribution
with a finite width. Here we calculate explicitly whether and how tensorial
models, such as the hydrodynamic Drude model and generalized nonlocal
optical response theory, follow this phenomenological description. We find
considerable differences, for example that nonlocal response functions,
in contrast to simple distributions, assume negative and complex values.
Moreover, nonlocal response regularizes some but not all diverging optical
near fields. We identify the scalar model that comes closest to the hydrodynamic
model. Interestingly, for the hydrodynamic Drude model we find
that actually only one third (1/3) of the free-electron response is smeared
out nonlocally. In that sense, nonlocal response is stronger for transverse
and scalar nonlocal response models, where the smeared-out fractions are
2/3 and 3/3, respectively. The latter two models seem to predict novel
plasmonic resonances also below the plasma frequency, in contrast to the
hydrodynamic model that predicts standing pressure waves only above the
plasma frequency.
November 2015.
Foerster resonance energy transfer rate in any dielectric nanophotonic medium with weak dispersion
Martijn Wubs and Willem L. Vos
New J. Phys. 18, 053037 (2016) |
download pdf |
ArXiv:1507.06212
| view abstract
Abstract: Motivated by the ongoing debate about nanophotonic control of Foerster resonance energy transfer (FRET), notably by the local density of optical states (LDOS), we study FRET and spontaneous emission in arbitrary nanophotonic media with weak dispersion and weak absorption in the frequency overlap range of donor and acceptor. This system allows us to obtain the following two new insights. Firstly, we derive that the FRET rate only depends on the static part of the Green function. Hence, the FRET rate is independent of frequency, in contrast to spontaneous-emission rates and LDOS that are strongly frequency dependent in nanophotonic media. Therefore, the position-dependent FRET rate and the LDOS at the donor transition frequency are completely uncorrelated for any nondispersive medium. Secondly, we derive an exact expression for the FRET rate as a frequency integral of the imaginary part of the Green function. This leads to very accurate approximation for the FRET rate that features the LDOS that is integrated over a huge bandwidth ranging from zero frequency to far into the UV. We illustrate these general results for the analytic model system of a pair of ideal dipole emitters—donor and acceptor—in the vicinity of an ideal mirror. We find that the FRET rate is independent of the LDOS at the donor emission frequency. Moreover, we observe that the FRET rate hardly depends on the frequency-integrated LDOS. Nevertheless, the FRET is controlled between inhibition and four times enhancement at distances close to the mirror, typically a few nm. Finally, we discuss the consequences of our results to applications of Foerster resonance energy transfer, for instance in quantum information processing.
July 2015.
Kerr nonlinearity and plasmonic bistability in graphene nanoribbons
Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, N. Asger Mortensen
Phys. Rev. B 92, 121407(R) (2015) |
download pdf |
download Supplementary Material |
ArXiv:1506.02856
| view abstract
Abstract: We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consistent iteration with linear steps using a real-space discretization. We derive a simple approximation for the resonance shifts in general graphene nanostructures, and obtain excellent agreement with numerics for moderately high field strengths. Near plasmonic resonances the nonlinearities are strongly enhanced due to field enhancement, and the total nonlinearity is significantly affected by the field inhomogeneity of the plasmonic excitation. Finally, we discuss the emergence of a plasmonic bistability which exists for frequencies redshifted relative to the linear resonance. Our results offer new insights into the role of nonlinear interaction in nanostructured graphene and paves the way for experimental investigation.
June 2015.
Multipole plasmons and their disappearance in few-nanometer silver nanoparticles
Søren Raza, Shima Kadkhodazadeh, Thomas Christensen, Marcel Di Vece, Martijn Wubs, N. Asger Mortensen, Nicolas Stenger
Nature Communications 6, 8788 (2015)
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download pdf |
download Supplementary Material |
ArXiv:1505.00594
| view abstract
Abstract: In electron energy-loss spectroscopy (EELS) of individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon (SP) resonance corresponding to higher angular momenta. We even observe both resonances for nanoparticle radii as small as 4 nm, where previously only the dipole resonance was assumed to play a role. Electron beams positioned outside of the particles mostly excite the dipole mode, but the higher-order resonance can even dominate the dipole peak when exciting at the particle surface, the usual choice for maximal EELS signal. This allows us to study the radius dependence of both resonances separately. For particles smaller than 4 nm, the higher-order SP mode disappears, in agreement with generalized nonlocal optical response (GNOR) theory, while the dipole resonance blueshift exceeds GNOR predictions. Unlike in optical spectra, multipole surface plasmons are important in EELS spectra even of ultra-small metallic nanoparticles.
May 2015.
Projected-Dipole Model for Quantum Plasmonics
Wei Yan, Martijn Wubs, N. Asger Mortensen
Phys. Rev. Lett. 115, 137403 (2015)
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download pdf |
download Supplementary Material
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ArXiv:1504.07113
| view abstract
Abstract: Quantum effects of plasmonic phenomena have been explored through ab-initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers we find quantum-corrections to the hybridization even in mesoscopic dimers as long as the gap is sub-nanometric itself.
April 2015.
Localized plasmons in graphene-coated nanospheres
Thomas Christensen, Antti-Pekka Jauho, Martijn Wubs, N. Asger Mortensen
Phys. Rev. B 91, 125414 (2015)
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download pdf
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ArXiv:1412.7042
| view abstract
Abstract: We present an analytical derivation of the electromagnetic response of a spherical object coated by a conductive film, here exemplified by a graphene coating. Applying the framework of Mie-Lorenz theory augmented to account for a conductive boundary condition, we derive the multipole scattering coefficients, modified essentially through the inclusion of an additive correction in numerator and denominator. By reductionist means, starting from the retarded response, we offer simple results in the quasistatic regime by analyzing the multipolar polarizability and associated dispersion equation for the localized plasmons. We consider graphene coatings of both dielectric and conducting spheres, where in the former case the graphene coating introduces the plasmons and in the latter case modifies in interesting ways the existing ones. Finally, we discuss our analytical results in the context of extinction cross-section and local density of states. Recent demonstrations of fabricated spherical graphene nanostructures make our study directly relevant to experiments.
December 2014.
Nonlocal optical response in metallic nanostructures (Topical Review)
Søren Raza, Sergey I. Bozhevolnyi, Martijn Wubs, N. Asger Mortensen
J. Phys.: Condens. Matter 27, 183204 (2015)
| download pdf
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ArXiv:1412.0942
| view abstract
Abstract: This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.
December 2014.
Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles
Weihua Wang, Thomas Christensen, Antti-Pekka Jauho, Kristian S. Thygesen, Martijn Wubs, N. Asger Mortensen
Scientific Reports 5, 9535 (2015)
| download pdf
| download supplementary information |
ArXiv:1410.0537
| view abstract
Abstract: Serving as a new two-dimensional plasmonic material, graphene has stimulated an intensive study of its optical properties which benefit from the unique electronic band structure of the underlying honeycomb lattice of carbon atoms. In classical electrodynamics, nanostructured graphene is commonly modeled by the computationally demanding problem of a three-dimensional conducting film of atomic-scale thickness. Here, we propose an efficient alternative two-dimensional electrostatic approach where all the calculation procedures are restricted to the plane of the graphene sheet. To explore possible quantum effects, we perform tight-binding calculations, adopting a random-phase approximation. We investigate the multiple plasmon modes in triangles of graphene, treating the optical response classically as well as quantum mechanically in the case of both armchair and zigzag edge termination of the underlying atomic lattice. Compared to the classical plasmonic spectrum which is "blind" to the edge termination, we find that the quantum plasmon frequencies exhibit blueshifts in the case of armchair edge termination, while redshifts are found for zigzag edges. Furthermore, we find spectral features in the zigzag case which are associated with electronic edge states not present for armchair termination. Merging pairs of such triangles into dimers, the plasmon hybridization leads to energy splitting in accordance with plasmon-hybridization theory, with a lower energy for the antisymmetric modes and a smaller splitting for modes with less confinement to the gap region. The hybridization appears strongest in classical calculations while the splitting is lower for armchair edges and even more reduced for zigzag edges. Our various results illustrate a surprising phenomenon: Even 20 nm large graphene structures clearly exhibit quantum plasmonic features due to atomic-scale details in the edge termination.
October 2014.
Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics
G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, M. Wubs
Nature Communications 6, 7132 (2015)
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ArXiv:1408.5862
| view abstract
| popular summary
Abstract: The standard hydrodynamic Drude model with hard-wall boundary conditions can give
accurate quantitative predictions for the optical response of noble-metal nanoparticles.
However, it is less accurate for other metallic nanosystems, where surface effects due to
electron density spill-out in free space cannot be neglected. Here we address the fundamental
question whether the description of surface effects in plasmonics necessarily requires a fully
quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model
(SC-HDM), where both the ground state and the excited state properties of an inhomogeneous
electron gas can be determined. With this method we are able to explain the
size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The
results we obtain are in good agreement with experiments and more advanced quantum
methods. The SC-HDM gives accurate results with modest computational effort, and can be
applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio
methods.
August 2014.
Classical and Quantum Plasmonics in Graphene Nanodisks: Role of Edge States
Thomas Christensen, Weihua Wang, Antti-Pekka Jauho, Martijn Wubs, and N. Asger Mortensen
Phys. Rev. B 90, 241414(R) (2014)
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ArXiv:1407.3920
| view abstract
Abstract: Edge states are ubiquitous for many condensed matter systems with multicomponent wave functions. For example, edge states play a crucial role in transport in zigzag graphene nanoribbons. Here, we report microscopic calculations of quantum plasmonics in doped graphene nanodisks with zigzag edges. We express the nanodisk conductivity as a sum of the conventional bulk conductivity, and a novel term, corresponding to a coupling between the edge and bulk states. We show that the edge states give rise to a redshift and broadening of the plasmon resonance, and that they often significantly impact the absorption efficiency. We further develop simplified models, incorporating nonlocal response within a hydrodynamical approach, which allow a semiquantitative description of plasmonics in the ultrasmall size regime. Furthermore, we show that the effect of hydrodynamic and edge-conductivity corrections scale identically, approximately with the inverse of the disk radius, highlighting their equatable importance. However, the polarization dependence is only given by fully microscopic models. The approach developed here should have many applications in other systems supporting edge states.
July 2014.
Nonlocal study of ultimate plasmon hybridization
Søren Raza, Martijn Wubs, Sergey I. Bozhevolnyi, and N. Asger Mortensen
Opt. Lett. 40, 839 (2015)
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ArXiv:1406.5091
| view abstract
Abstract: Within our recently proposed generalized nonlocal optical response (GNOR) model, we revisit the fundamental problem of an optically excited plasmonic dimer. The dimer consists of two identical cylinders separated by a nanometre-sized gap. We consider the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics we determine a simple analytical equation for the resonance energies of the bonding plasmon modes of the touching dimer.
June 2014.
Nonlocal response of metallic nanospheres probed by light, electrons, and atoms
Thomas Christensen, Wei Yan, Søren Raza, Antti-Pekka Jauho, N. Asger Mortensen, and Martijn Wubs
ACS Nano 8, 1745 (2014)
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ArXiv:1403.1100
| view abstract
Abstract: Inspired by recent measurements on individual metallic nanospheres that can not be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model and Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single blueshifted surface plasmon, but also an infinite series of bulk plasmons that has no counterpart in a local-response approximation. We show that these increasingly blueshifted multipole plasmons become spectrally more prominent at shorter probe-to-surface separations and for decreasing nanosphere radii. For selected metals we predict hydrodynamic multipolar plasmons to be measurable on single nanospheres.
January 2014.
A generalized non-local optical response theory for plasmonic nanostructures
N. Asger Mortensen, Søren Raza, Martijn Wubs, Thomas Søndergaard, Sergey I. Bozhevolnyi
Nature Commun. 5, 3809 (2014) |
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ArXiv:1312.7190 | view abstract
Abstract: Metallic nanostructures exhibit a multitude of optical resonances associated with localized surface plasmon excitations. Recent observations of plasmonic phenomena at the sub-nanometer to atomic scale have stimulated the development of various sophisticated theoretical approaches for their description. Here instead we present a comparatively simple semiclassical generalized nonlocal optical response (GNOR) theory that unifies quantum-pressure convection effects and induced-charge diffusion kinetics, with a concomitant complex-valued GNOR parameter. Our theory explains surprisingly well both the frequency shifts and size-dependent damping in individual metallic nanoparticles (MNPs) as well as the observed broadening of the cross-over regime from bonding-dipole plasmons to charge-transfer plasmons in MNP dimers, thus unraveling a classical broadening mechanism that even dominates the widely anticipated short-circuiting by quantum tunneling. We anticipate that the GNOR theory can be successfully applied in plasmonics to a wide class of conducting media, including doped semiconductors and low-dimensional materials such as graphene.
December 2013.
Extremely confined gap surface plasmon modes excited by electrons
S. Raza, N. Stenger, A. Pors, T. Holmgaard, S. Kadkhodazadeh, J. B. Wagner, K. Pedersen, M. Wubs, S. I. Bozhevolnyi, N. A. Mortensen
Nature Commun. 5, 4125 (2014) |
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ArXiv:1312.4760 | view abstract
Abstract: High-spatial and energy resolution electron energy-loss spectroscopy (EELS) can be used for detailed characterization of localized and propagating surface-plasmon excitations in metal nanostructures, giving insight into fundamental physical phenomena and various plasmonic effects. Here, applying EELS to ultra-sharp convex grooves in gold, we directly probe extremely confined gap surface-plasmon (GSP) modes excited by swift electrons in nanometre-wide gaps. We reveal the resonance behaviour associated with the excitation of the antisymmetric GSP mode for extremely small gap widths, down to ~5 nm. We argue that excitation of this mode, featuring very strong absorption, has a crucial role in experimental realizations of non-resonant light absorption by ultra-sharp convex grooves with fabrication-induced asymmetry. The occurrence of the antisymmetric GSP mode along with the fundamental GSP mode exploited in plasmonic waveguides with extreme light confinement is a very important factor that should be taken into account in the design of nanoplasmonic circuits and devices.
December 2013.
Nonlocal modification and quantum optical generalization of effective-medium theory for metamaterials
Martijn Wubs, Wei Yan, Ehsan Amooghorban, and N. Asger Mortensen
Proc. SPIE 8806, 88061F (2013) |
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Abstract: A well-known challenge for fabricating metamaterials is to make unit cells significantly smaller than the operating wavelength of light, so one can be sure that effective-medium theories apply. But do they apply? Here we show that nonlocal response in the metal constituents of the metamaterial leads to modified effective parameters for strongly subwavelength unit cells. For infinite hyperbolic metamaterials, nonlocal response gives a very large finite upper bound to the optical density of states that otherwise would diverge. Moreover, for finite hyperbolic metamaterials we show that nonlocal response affects their operation as superlenses, and interestingly that sometimes nonlocal theory predicts the better imaging. Finally, we discuss how to describe metamaterials effectively in quantum optics. Media with loss or gain have associated quantum noise, and the question is whether the effective index is enough to describe this quantum noise effectively. We show that this is true for passive metamaterials, but not for metamaterials where loss is compensated by linear gain. For such loss-compensated metamaterials we present a quantum optical effective medium theory with an effective noise photon distribution as an additional parameter. Interestingly, we find that at the operating frequency, metamaterials with the same effective index but with different amounts of loss compensation can be told apart in quantum optics.
September 2013.
Green's function surface-integral method for nonlocal response of plasmonic nanowires
in arbitrary dielectric environments
Wei Yan, N. Asger Mortensen, and Martijn Wubs
Phys. Rev. B 88, 155414 (2013) |
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ArXiv:1307.7183
| view abstract
Abstract: We develop a nonlocal-response generalization to the Green-function surface-integral method (GSIM), also known as the boundary-element method (BEM). This numerically light method can accurately describe the linear hydrodynamic nonlocal response of arbitrarily shaped plasmonic nanowires in arbitrary dielectric backgrounds. All previous general-purpose methods for nonlocal response are bulk methods. We also expand the possible geometries to which the usual local-response GSIM can be applied, by showing how to regularize singularities that occur in the surface integrals when the nanoparticles touch a dielectric substrate. The same regularization works for nonlocal response. Furthermore, an effective theory is developed to explain the numerically observed nonlocal effects. The nonlocal frequency blueshift of a cylindrical nanowire in an inhomogeneous background generally increases as the nanowire radius and the longitudinal wavenumber become smaller, or when the effective background permittivity or the mode inhomogeneity increase. The inhomogeneity can be expressed in terms of an effective angular momentum of the surface-plasmon mode. We compare local and nonlocal response of free-standing nanowires, and of nanowires close to and on top of planar dielectric substrates. Especially for the latter geometry, considerable differences in extinction cross sections are found for local as compared to nonlocal response, similar to what is found for plasmonic dimer structures.
July 2013.
Blueshift of the surface plasmon resonance in silver nanoparticles: substrate effects
Søren Raza, Wei Yan, Nicolas Stenger, Martijn Wubs, and N. Asger Mortensen
Opt. Express 21, 27344 (2013) |
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ArXiv:1307.6983
| view abstract
Abstract: We study the blueshift of the surface plasmon (SP) resonance energy of isolated Ag nanoparticles with decreasing particle diameter, which we recently measured using electron energy loss spectroscopy (EELS). As the particle diameter decreases from 26 down to 3.5 nm, a large blueshift of 0.5 eV of the SP resonance energy is observed. In this paper, we base our theoretical interpretation of our experimental findings on the nonlocal hydrodynamic model, and compare the effect of the substrate on the SP resonance energy to the approach of an effective homogeneous background permittivity. We derive the nonlocal polarizability of a small metal sphere embedded in a homogeneous dielectric environment, leading to the nonlocal generalization of the classical Clausius-Mossotti factor. We also present an exact formalism based on multipole expansions and scattering matrices to determine the optical response of a metal sphere on a dielectric substrate of finite thickness, taking into account retardation and nonlocal effects. We find that the substrate-based calculations show a similar-sized blueshift as calculations based on a sphere in a homogeneous environment, and that they both agree qualitatively with the EELS measurements.
July 2013.
Nonlocal response in thin-film waveguides: loss versus nonlocality and
breaking of complementarity
Søren Raza, Thomas Christensen, Martijn Wubs, Sergey I. Bozhevolnyi, and N. Asger Mortensen
Phys. Rev. B 88, 115401 (2013) |
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ArXiv:1305.1185
| view abstract
Abstract: We investigate the effects of nonlocal response on the surface-plasmon polariton guiding properties of the metal-insulator (MI), metal-insulator-metal (MIM), and insulator-metal-insulator (IMI) waveguides. The nonlocal effects are described by a linearized hydrodynamic model, which includes the Thomas-Fermi internal kinetic energy of the free electrons in the metal. We derive the nonlocal dispersion relations of the three waveguide structures taking into account also retardation and interband effects, and examine the delicate interplay between nonlocal response and absorption losses in the metal. We also show that nonlocality breaks the complementarity of the MIM and IMI waveguides found in the non-retarded limit.
May 2013.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
Wei Yan, N. Asger Mortensen, and Martijn Wubs
Opt. Express 21, 15026 (2013) |
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ArXiv:1302.3733
| view abstract
Abstract: We investigate the effects of hydrodynamic nonlocal response
in hyperbolic metamaterials (HMMs), focusing on the experimentally
realizable parameter regime where unit cells are much smaller than an
optical wavelength but much larger than the wavelengths of the longitudinal
pressure waves of the free-electron plasma in the metal constituents. We
derive the nonlocal corrections to the effective material parameters analytically,
and illustrate the noticeable nonlocal effects on the dispersion curves
numerically. As an application, we find that the focusing characteristics of
a HMM lens in the local-response approximation and in the hydrodynamic
Drude model can differ considerably. In particular, the optimal frequency
for imaging in the nonlocal theory is blueshifted with respect to that in
the local theory. Thus, to detect whether nonlocal response is at work in a
hyperbolic metamaterial, we propose to measure the near-field distribution
of a hyperbolic metamaterial lens.
February 2013.
Cooperative fluorescence from a strongly driven dilute cloud of atoms
J. R. Ott, M. Wubs, P. Lodahl, N. A. Mortensen, and R. Kaiser
Physical Review A 87, 061801(R) (2013)
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ArXiv:1301.7575
| view abstract
Abstract: We investigate cooperative fluorescence in a dilute cloud of strongly driven two-level emitters. Starting from the Heisenberg equations of motion, we compute the first-order scattering corrections to the saturation of the excited-state population and to the resonance-fluorescence spectrum, which both require going beyond the state-of-the-art linear-optics approach to describe collective phenomena. A dipole blockade is observed due to long range dipole-dipole coupling that vanishes at stronger driving fields. Furthermore, we compute the inelastic component of the light scattered by a cloud of many atoms and find that the Mollow triplet is affected by cooperativity. In a lobe around the forward direction, the inelastic Mollow triplet develops a spectral asymmetry, observable under experimental conditions.
January 2013.
Nonlocal response in plasmonic waveguiding with extreme light confinement
G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen
Nanophotonics 2, 161 (2013) |
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ArXiv:1212.4925
| view abstract
Abstract: We present a novel wave equation for linearized plasmonic response, obtained by combining the coupled real-space differential equations for the electric field and current density. Nonlocal dynamics are fully accounted for, and the formulation is very well suited for numerical implementation, allowing us to study waveguides with subnanometer cross-sections exhibiting extreme light confinement. We show that groove and wedge waveguides have a fundamental lower limit in their mode confinement, only captured by the nonlocal theory. The limitation translates into an upper limit for the corresponding Purcell factors, and thus has important implications for quantum plasmonics.
December 2012.
Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS
S. Raza, N. Stenger, S. Kadkhodazadeh, S.V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, N.A. Mortensen
Nanophotonics 2, 131 (2013) |
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ArXiv:1210.2535
| view abstract
Abstract: We study the surface plasmon (SP) resonance energy of isolated spherical Ag nanoparticles in the diameter range 3.5-26 nm with monochromated electron energy-loss spectroscopy. A significant blueshift of the SP resonance energy of 0.5 eV is measured when the particle size decreases from 26 down to 3.5 nm. We interpret the observed blueshift using three models for a metallic sphere embedded in homogeneous background material: a classical Drude model with a homogeneous electron density profile in the metal, a semiclassical model corrected for an inhomogeneous electron density associated with quantum confinement, and a semiclassical nonlocal hydrodynamic description of the electron density. We find that the latter two models provide a qualitative explanation for the observed blueshift, but the theoretical predictions show smaller blueshifts than observed experimentally. We attribute the larger measured blueshift to effects due to the presence of the substrate, which breaks the symmetry of a particle embedded in a homogeneous medium.
October 2012.
Quantum optical effective-medium theory for loss-compensated metamaterials
Ehsan Amooghorban, N. Asger Mortensen, and Martijn Wubs
Phys. Rev. Lett. 110, 153602 (2013) |
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ArXiv:1208.0461
| view abstract
| Press:
www.technology.org
Abstract: A central aim in metamaterial research is to engineer sub-wavelength unit cells that give rise to desired effective-medium properties and parameters, such as a negative refractive index. Ideally one can disregard the details of the unit cell and employ the effective description instead. A popular strategy to compensate for the inevitable losses in metallic components of metamaterials is to add optical gain material. Here we study the quantum optics of such loss-compensated metamaterials at frequencies for which effective parameters can be unambiguously determined. We demonstrate that the usual effective parameters are insufficient to describe the propagation of quantum states of light. Furthermore, we propose a quantum-optical effective-medium theory instead and show that it correctly predicts the properties of the light emerging from loss-compensated metamaterials.
August 2012.
Nanoplasmonics beyond Ohm's law
N.A. Mortensen, G. Toscano, S. Raza, N. Stenger, W. Yan, A.-P. Jauho, S. Xiao, M. Wubs
AIP Conf. Proc. 1475, 28 (2012)
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ArXiv:1208.0146
| view abstract
Abstract: In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behavior with important consequences for e.g. field-enhancement and extinction cross sections. We report on our most recent developments of a real-space formulation of an equation-of-motion that goes beyond the common local-response approximation and use of Ohm's law as the central constitutive equation. The electron gas is treated within a semi-classical hydrodynamic model with the emergence of a new intrinsic length scale. We briefly review the new governing wave equations and give examples of applying the nonlocal framework to calculation of extinction cross sections and field enhancement in isolated particles, dimers, and corrugated surfaces.
August 2012.
Nanophotonic control of the Förster resonance energy transfer efficiency
Christian Blum, Niels Zijlstra, Ad Lagendijk, Martijn Wubs, Allard P. Mosk, Vinod Subramaniam, and Willem L. Vos
Physical Review Letters 109, 203601 (2012) (cover article)
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ArXiv:1207.2272
| view abstract |
Research Highlight in Nature Materials and
Editor's Choice in Science.
| Press: phys.org,
nanowerk.com,
BioOpticsWorld.com,
videnskab.dk (danish), and
forskning.no (norwegian).
Abstract: We have studied the influence of the local density of optical states (LDOS) on the rate and efficiency of Förster resonance energy transfer (FRET) from a donor to an acceptor. The donors and acceptors are dye molecules that are separated by a short strand of double-stranded DNA. The LDOS is controlled by carefully positioning the FRET pairs near a mirror. We find that the energy transfer efficiency changes with LDOS, and that, in agreement with theory, the energy transfer rate is independent of the LDOS, which allows one to quantitatively control FRET systems in a new way. Our results imply a change in the characteristic Förster distance, in contrast to common lore that this distance is fixed for a given FRET pair.
July 2012.
Hyperbolic metamaterials: nonlocal response regularizes broadband supersingularity
Wei Yan, Martijn Wubs, and N. Asger Mortensen
Physical Review B 86, 205429 (2012) |
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ArXiv:1204.5413
| view abstract
Abstract: We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small wavevectors we find differences for the hyperbolic dispersion. Moreover, the size of the unit cell influences effective parameters of the metamaterial even in the deep sub-wavelength regime. Finally, instead of the broadband super-singularity in the local density of states, we predict a large but finite maximal enhancement proportional to the inverse cube of the Fermi velocity.
April 2012.
Surface-enhanced Raman spectroscopy (SERS): nonlocal limitations
Giuseppe Toscano, Søren Raza, Sanshui Xiao, Martijn Wubs, Antti-Pekka Jauho, Sergey I. Bozhevolnyi, and N. Asger Mortensen
Optics Letters 37, 2538 (2012) |
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ArXiv:1203.1310
| view abstract
Abstract: Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and fundamental limitations on the field enhancement with important consequences for our understanding of SERS. The intrinsic length scale of the electron gas serves to smear out assumed field singularities, leaving the SERS enhancement factor finite even for geometries with infinitely sharp features. For silver nano-groove structures, mimicked by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding ten orders of magnitude (10^10).
March 2012.
Refractive-index sensing with ultra-thin plasmonic nanotubes
Søren Raza, Giuseppe Toscano, Antti-Pekka Jauho, N. Asger Mortensen, and Martijn Wubs
Plasmonics 8, 193 (2013) |
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ArXiv:1203.0575
| view abstract
Abstract: We study the refractive-index sensing properties of plasmonic nanotubes with a dielectric core and ultra-thin metal shell. The few-nm thin metal shell is described by both the usual Drude model and the nonlocal hydrodynamic model to investigate the effects of nonlocality. We derive an analytical expression for the extinction cross section and show how sensing of the refractive index of the surrounding medium and the figure-of-merit are affected by the shape and size of the nanotubes. Comparison with other localized surface plasmon resonance sensors reveals that the nanotube exhibits superior sensitivity and comparable figure-of-merit.
March 2012.
Are there novel resonances in nanoplasmonic structures due
to nonlocal response?
Martijn Wubs, Søren Raza, Giuseppe Toscano, Antti-Pekka Jauho, and N. Asger Mortensen
Proc. SPIE 8260, 82601E (2012) |
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| view abstract
Abstract: In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behaviour with resulting important consequences for e.g. field-enhancement and extinction cross sections. Here we report on nonlocal resonances in the hydrodynamical Drude model for plasmonic nanostructures that have no counterpart in the local-response Drude model. Even though there are no additional resonances in the visible
due to nonlocal response, plasmonic field enhancements are affected by nonlocal response. We present both
analytical results for simple geometries and our numerical implementation for arbitrary geometries, and address computational issues related to the several length scales involved.
December 2011.
Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response
Giuseppe Toscano, Søren Raza, Antti-Pekka Jauho, N. Asger Mortensen, and Martijn Wubs
Opt. Express 20, 4176 (2012)
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ArXiv:1110.1651
| view abstract
Abstract: We study the effect of nonlocal optical response on the optical properties of metallic nanowires, by numerically implementing the hydrodynamical Drude model for arbitrary nanowire geometries. We first demonstrate the accuracy of our frequency-domain finite-element implementation by benchmarking it in a wide frequency range against analytical results for the extinction cross section of a cylindrical plasmonic nanowire. Our main results concern more complex geometries, namely cylindrical and bow-tie nanowire dimers that can strongly enhance optical fields. For both types of dimers we find that nonlocal response can strongly affect both the field enhancement in between the dimers and their respective extinction cross sections. In particular, we give examples of blueshifted maximal field enhancements near hybridized plasmonic dimer resonances that are still large but nearly two times smaller than in the usual local-response description. For the same geometry at a fixed frequency, the field enhancement and cross section can also be significantly more enhanced in the nonlocal-response model.
October 2011.
Scattering Induced Quantum Interference of Multiple Quantum Optical States
Johan R. Ott, M. Wubs, N. Asger Mortensen, and Peter Lodahl
AIP Conf. Proc. 1398, 82 (2011) |
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Abstract: Using a discrete mode theory for propagation of quantum optical states, we investigate the consequences of multiple scattering on the degree of quadrature entanglement and quantum interference. We report that entangled states can be created by multiple-scattering. We furthermore show that quantum interference induced by the transmission of quantized light through a multiple-scattering medium will persist even after averaging over an ensemble of scattering samples.
October 2011.
Coherent single-photon absorption by single emitters coupled to 1D nanophotonic waveguides
Yuntian Chen, Martijn Wubs, Jesper Mørk, A. Femius Koenderink
New Journal of Physics 13, 103010 (2011) |
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ArXiv:1107.0120
| view abstract
| popular science article on videnskab.dk (in danish)
Abstract: We study the dynamics of single-photon absorption by a single emitter coupled to a one-dimensional waveguide that simultaneously provides channels for spontaneous emission (SE) decay and a channel for the input photon. We have developed a time-dependent theory that allows us to specify any input single-photon wavepacket guided by the waveguide as the initial condition, and calculate the excitation probability of the emitter, as well as the time evolution of the transmitted and reflected fields. For single-photon wavepackets with a Gaussian spectrum and temporal shape, we obtain analytical solutions for the dynamics of absorption, with maximum atomic excitation near 40 percent. We furthermore propose a terminated waveguide to aid the single-photon absorption. We found that for an emitter placed at an optimal distance from the termination, the maximum atomic excitation due to an incident single-photon wavepacket can exceed 70 percent. This high value is a direct consequence of the high SE beta-factor for emission into the waveguide. Finally, we have also explored whether waveguide dispersion could aid single-photon absorption by pulse shaping. For a Gaussian input wavepacket, we found that the absorption efficiency can be improved by a further 4 percent by engineering the dispersion. Efficient single-photon absorption by a single emitter has potential applications in quantum communication and quantum computation.
July 2011.
Surface plasmon modes of a single silver nanorod: an electron energy loss study
Olivia Nicoletti, Martijn Wubs, N. Asger Mortensen, Wilfried Sigle, Peter A. van Aken, Paul A. Midgley
Opt. Express 19, 15371 (2011) |
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ArXiv:1106.4533
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Abstract: We present an electron energy loss study using energy filtered TEM of spatially resolved surface plasmon excitations on a silver nanorod of aspect ratio 14.2 resting on a 30 nm thick silicon nitride membrane. Our results show that the excitation is quantized as resonant modes whose intensity maxima vary along the nanorod's length and whose wavelength becomes compressed towards the ends of the nanorod. Theoretical calculations modelling the surface plasmon response of the silver nanorod-silicon nitride system show the importance of including retardation and substrate effects in order to describe accurately the energy dispersion of the resonant modes.
June 2011.
Unusual resonances in nanoplasmonic structures due to nonlocal response
Søren Raza, Giuseppe Toscano, Antti-Pekka Jauho, Martijn Wubs, N. Asger Mortensen
Physical Review B 84, 121412(R) (2011)
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ArXiv:1106.2175
| view abstract
Abstract: We study the nonlocal response of a confined electron gas within the hydrodynamical Drude model. We address the question whether plasmonic nanostructures exhibit nonlocal resonances that have no counterpart in the local-response Drude model. Avoiding the usual quasi-static approximation, we find that such resonances do indeed occur, but only above the plasma frequency. Thus the recently found nonlocal resonances at optical frequencies for very small structures, obtained within quasi-static approximation, are unphysical. As a specific example we consider nanosized metallic cylinders, for which extinction cross sections and field distributions can be calculated analytically.
June 2011.
Casimir forces in multilayer magnetodielectrics with both gain and loss
Ehsan Amooghorban, Martijn Wubs, N. Asger Mortensen, and Fardin Kheirandish
Physical Review A 84, 013806 (2011)
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ArXiv:1104.1500
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Abstract: A path-integral approach to the quantization of the electromagnetic field in a linearly amplifying magnetodielectric medium is presented. Two continua of inverted harmonic oscillators are used to describe the polarizability and magnetizability of the amplifying medium. The causal susceptibilities of the amplifying medium, with negative imaginary parts in finite frequency intervals, are identified and their relation to microscopic coupling functions are determined. By carefully relating the two-point functions of the field theory to the optical Green functions, we calculate the Casimir energy and Casimir forces for a multilayer magnetodielectric medium with both gain and loss. We point out the essential differences with a purely passive layered medium. For a single layer, we find different bounds on the Casimir force for fully amplifying and for lossy media. The force is attractive in both cases, also if the medium exhibits negative refraction. From our Lagrangian we also derive by canonical quantization the postulates of the phenomenological theory of amplifying magnetodielectrics.
April 2011.
Mode expansions in the quantum electrodynamics of photonic media with disorder
M. Wubs and N. A. Mortensen
Photonics and Nanostructures 10, 296 (2012)
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ArXiv:1101.5556
| view abstract
Abstract: We address two issues in the quantum electrodynamical description of photonic media with some disorder, neglecting material
dispersion. When choosing a gauge in which the static potential vanishes, the normal modes of the medium with disorder satisfy
another transversality condition than the modes of the ideal medium. Our first result is an integral equation for optical modes
such that all perturbation-theory solutions automatically satisfy the desired transversality condition. Secondly, when expanding the
vector potential for the medium with disorder in terms of the normal modes of the ideal structure, we find the gauge transformation
that makes the static potential zero, thereby generalizing work by Glauber and Lewenstein [ Phys. Rev. A 43, 467 (1991) ]. Our
results are relevant for the quantum optics of disordered photonic crystals.
28 January 2011.
Field enhancement at metallic interfaces due to quantum confinement
Z. Fatih Öztürk, Sanshui Xiao, Min Yan, Martijn Wubs, Antti-Pekka Jauho, Niels Asger Mortensen
Journal of Nanophotonics 5, 051602 (2011) |
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ArXiv:1012.0714
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Abstract: We point out an apparently overlooked consequence of the boundary conditions
obeyed by the electric displacement vector at air-metal interfaces: the continuity of the normal component combined with the quantum mechanical penetration of the electron gas in the air implies the existence of a surface on which the dielectric function vanishes. This, in turn, leads to an enhancement of the normal component of the total electric field. We study this effect for a planar metal surface, with the inhomogeneous electron density accounted for by a Jellium model. We also illustrate the effect for equilateral triangular nano-islands via numerical solutions of the appropriate Maxwell equations, and show that the field enhancement is several orders of magnitude larger than what the conventional theory predicts.
03 December 2010.
Surface plasmon wave adaptor designed with transformation optics
Jingjing Zhang, Sanshui Xiao, Martijn Wubs and Niels Asger Mortensen
ACS Nano 5, 4359 (2011)
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Abstract: On the basis of transformation optics, we propose the design of a surface plasmon wave adapter which confines surface plasmon waves on non-uniform metal surfaces and enables adiabatic mode transformation of surface plasmon polaritons with very short tapers. This adapter can be simply achieved with homogeneous anisotropic naturally occurring materials or subwavelength grating-structured dielectric materials. Full wave simulations based on a finite-element method have been performed to validate our proposal.
October 2010.
Plasmonic nanostructures: local versus nonlocal response
Giuseppe Toscano, Martijn Wubs, Sanshui Xiao, Min Yan, Z. Fatih Ozturk, Antti-Pekka Jauho, and N. Asger Mortensen
Proc. SPIE 7757, 77571T (2010); doi:10.1117/12.860774 |
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Abstract: We study the importance of taking the nonlocal optical response of metals into account for accurate determination of optical properties of nanoplasmonic structures. Here we focus on the computational physics aspects of this problem, and in particular we report on the nonlocal-response package that we wrote for state-of the art numerical software, enabling us to take into account the nonlocal material response of metals for any arbitrarily shaped
nanoplasmonic structures, without much numerical overhead as compared to the standard local response. Our method is a frequency-domain method, and hence it is sensitive to possible narrow resonances that may arise due to strong electronic quantum confinement in the metal. This feature allows us to accurately determine which geometries are strongly affected by nonlocal response, for example regarding applications based on electric field
enhancement properties for which metal nanostructures are widely used.
1 August 2010.
Instantaneous coherent destruction of tunneling and fast quantum state preparation for strongly pulsed spin qubits in diamond
Martijn Wubs
Chemical Physics 375, 163 (2010) |
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ArXiv:1001.4614
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Abstract: Qubits driven by resonant strong pulses are studied and a parameter regime is explored in which the dynamics can be solved in closed form. Instantaneous coherent destruction of tunneling can be seen for longer pulses, whereas shorter pulses allow a fast preparation of the qubit state. Results are compared with recent experiments of pulsed nitrogen-vacancy center spin qubits in diamond.
26 January 2010.
Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits
D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen
Physical Review Letters 105, 210501 (2010) |
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Supplementary Information
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ArXiv:1001.4048
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Popular summary
Abstract: We propose a method to achieve coherent coupling between Nitrogen-vacancy (NV) centers in
diamond and superconducting (SC) flux qubits. The resulting coupling can be used to create a
coherent interaction between the spin states of distant NV centers mediated by the flux qubit. Furthermore,
the magnetic coupling can be used to achieve a coherent transfer of quantum information
between the flux qubit and an ensemble of NV centers. This enables a long-term memory for a SC
quantum processor and possibly an interface between SC qubits and light.
22 January 2010.
Multimode model for projective photon-counting measurements
Rosa Tualle-Brouri, Alexei Ourjoumtsev, Aurelien Dantan, Philippe Grangier, Martijn Wubs, and Anders S. Sørensen
Physical Review A 80, 013806 (2009) |
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ArXiv:0902.2867
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Abstract: We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-gaussian states are produced conditionally. These are useful states for continuous-variable quantum information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric downconversion, thereby improving the analysis of existing experimental results. The main improvement is that spatial and frequency filters before the photon detector are taken into account explicitly. We find excellent agreement with previously published experimental results, using fewer free parameters than before, and discuss the implications of our analysis for the optimized production of states with negative Wigner functions.
17 February 2009.
Fast initial qubit dephasing and the influence of substrate dimensions on error correction rates
Roland Doll, Peter Hanggi, Sigmund Kohler, and Martijn Wubs
European Physical Journal B 68, 523 (2009) |
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ArXiv:0807.2555
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Abstract: Keeping single-qubit quantum coherence above some threshold value not far below unity is a prerequisite for fault-tolerant quantum error correction (QEC). We study the initial dephasing of solid-state qubits in the independent-boson model, which describes well recent experiments on quantum dot (QD) excitons both in bulk and in substrates of reduced geometry such as nanotubes. Using explicit expressions for the exact coherence dynamics, a minimal QEC rate is identified in terms of error threshold, temperature, and qubit-environment coupling strength. This allows us to systematically study the benefit of a current trend towards substrates with reduced dimensions.
16 July 2008.
Fidelity and Entanglement of a Spatially Extended Linear Three-Qubit Register
Roland Doll, Martijn Wubs, Sigmund Kohler, and Peter Hanggi
International Journal of Quantum Information 6 , 681 (2008)
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ArXiv:0802.1930
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Abstract: We study decoherence of a three-qubit array coupled to substrate phonons. Assuming an initial three-qubit entangled state that would be decoherence-free for identical qubit positions, allows us to focus on non-Markovian effects of the inevitable spatial qubit separation. It turns out that the coherence is most affected when the qubits are regularly spaced. Moreover, we find that up to a constant scaling factor, two-qubit entanglement is not influenced by the presence of the third qubit, even though all qubits interact via the phonon field.
18 February 2008.
Bath-independent transition probabilities in the dissipative Landau-Zener problem
Sigmund Kohler, Peter Hanggi, and Martijn Wubs
in:
Path Integrals: New Trends and Perspectives, edited by W. Janke and A. Pelster
(World Scientific, Singapore, 2008), p. 456-461 |
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Abstract: We study Landau-Zener transitions of a two-level system that is coupled to a quantum heat bath at zero temperature. In particular, we reveal that for a whole class of models, the probability for a nonadiabatic transition is bath-independent.
2 January 2008.
On the conundrum of deriving exact solutions from approximate master
equations
R. Doll, D. Zueco, M. Wubs, S. Kohler, and P. Hanggi
Chemical Physics 347 , 243 (2008)
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ArXiv:0707.3938
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Abstract: We derive the exact time-evolution for a general quantum system under the influence of a bosonic bath that causes pure phase noise and demonstrate that for a Gaussian initial state of the bath, the exact result can be obtained also within a perturbative time-local master equation approach already in second order of the system-bath coupling strength. We reveal that this equivalence holds if the initial state of the bath can be mapped to a Gaussian phase-space distribution function. Moreover, we discuss the relation to the standard Bloch-Redfield approach.
11 September 2007.
Incomplete pure dephasing of N-qubit entangled W states
R. Doll, M. Wubs, P. Hanggi, and S. Kohler
Physical Review B 76 , 045317 (2007)
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ArXiv:cond-mat/0703075
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Abstract: We consider qubits in a linear arrangement coupled to a bosonic field which acts as a quantum heat bath and causes decoherence. By taking the spatial separation of the qubits explicitly into account, the reduced qubit dynamics acquires an additional non-Markovian element. We investigate the exact time evolution of an entangled many-qubit W state, which for vanishing qubit separation remains robust under pure dephasing. For finite separation, by contrast, the dynamics is no longer decoherence-free. On the other hand, spatial noise correlations may prevent complete dephasing. While a standard Bloch-Redfield master equation fails to describe this behavior even qualitatively, we propose instead a widely applicable causal master equation. Here we employ it to identify and characterize decoherence-poor subspaces. Consequences for quantum error correction are discussed.
17 July 2007.
Bell-state generation in circuit QED via Landau-Zener tunneling
Peter Hanggi, Martijn Wubs, Sigmund Kohler, Keiji Saito, and Yosuke Kayanuma
AIP Conference Proceedings Volume 922, pp. 501-506
NOISE AND FLUCTUATIONS: 19th International Conference on Noise and Fluctuations; ICNF 2007
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Abstract: A qubit may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic oscillators. First we show that for a qubit coupled to one oscillator, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of qubit-oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Second, for a qubit coupled to two cavities, we show that Landau-Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. Finally, for a qubit coupled to an environment or bath we propose to employ dissipative Landau-Zener sweeps of the qubit for the detection of bath properties. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the qubit, by summing all orders of the corresponding series in time-dependent perturbation theory.
13 July 2007.
Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior
K. Saito, M. Wubs, S. Kohler, Y. Kayanuma, and P. Hanggi
Physical Review B 75, 214308 (2007)
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ArXiv:cond-mat/0703596
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Abstract: We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.
29 June 2007.
Entanglement creation in circuit QED via Landau-Zener sweeps
M. Wubs, S. Kohler, and P. Hanggi
Physica E 40, 187 (2007)
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ArXiv:cond-mat/0703425
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Abstract: A qubit may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic oscillators. We show that for a qubit coupled to one oscillator, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of qubit-oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a qubit coupled to two cavities, we show that Landau-Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the qubit, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the oscillator frequencies, both inside and outside the regime where a rotating-wave approximation is valid.
24 May 2007.
Gauging a quantum heat bath with dissipative Landau-Zener transitions
M. Wubs, K. Saito, S. Kohler, P. Hanggi, and Y. Kayanuma
Physical Review Letters 97, 200404 (2006)
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ArXiv:cond-mat/0608333
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Abstract: We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
17 November 2006.
Limitation of entanglement due to spatial qubit separation
R. Doll, M. Wubs, P. Hanggi and S. Kohler
Europhysics Letters 76, 547 (2006)
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ArXiv:cond-mat/0608526
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Abstract: We consider spatially separated qubits coupled to a thermal bosonic field that causes pure dephasing. Our focus is on the entanglement of two Bell states which for vanishing separation are known as robust and fragile entangled states. The reduced two-qubit dynamics is solved exactly and explicitly. Our results allow us to gain information about the robustness of two-qubit decoherence-free subspaces with respect to physical parameters such as temperature, qubit-bath coupling strength and spatial separation of the qubits. Moreover, we clarify the relation between single-qubit coherence and two-qubit entanglement and identify parameter regimes in which the terms robust and fragile are no longer appropriate.
15 November 2006.
Quantum state preparation in circuit QED via Landau-Zener tunneling
K. Saito, M. Wubs, S. Kohler, P. Hanggi, and Y. Kayanuma
Europhysics Letters 76, 22 (2006)
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ArXiv:cond-mat/0603188
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Abstract: We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement.
1 October 2006.
Landau-Zener transitions in qubits controlled by electromagnetic fields
M. Wubs, K. Saito, S. Kohler, Y. Kayanuma, and P. Hanggi
New Journal of Physics 7, 218 (2005)
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ArXiv:cond-mat/0508156
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Abstract: We investigate the influence of a dipole interaction with a classical radiation field on a qubit during a continuous change of a control parameter. In particular, we explore the non-adiabatic transitions that occur when the qubit is swept with linear speed through resonances with the time-dependent interaction. Two classic problems come together in this model: the Landau-Zener (LZ) and the Rabi problem. The probability of LZ transitions now depends sensitively on the amplitude, the frequency and the phase of the Rabi interaction. The influence of the static phase turns out to be particularly strong, since this parameter controls the time-reversal symmetry of the Hamiltonian. In the limits of large and small frequencies, analytical results obtained within a rotating-wave approximation compare favourably with a numerically exact solution. We discuss physical realizations in microwave optics, quantum dots and molecular nanomagnets.
11 October 2005.
Multiple-scattering approach to dipole-dipole interactions and superradiance in inhomogeneous dielectrics
M. Wubs, L. G. Suttorp, and A. Lagendijk
Physical Review A 70, 053823 (2004)
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ArXiv:quant-ph/0409115
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Abstract: The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multiatom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.
29 November 2004.
Field quantization in inhomogeneous absorptive dielectrics
L. G. Suttorp and M. Wubs
Physical Review A 70, 013816 (2004)
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ArXiv:quant-ph/0407045
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Abstract: The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.
30 July 2004.
Spontaneous-emission rates in finite photonic crystals of plane scatterers
M. Wubs, L. G. Suttorp, and A. Lagendijk
Physical Review E 69, 016616 (2004)
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ArXiv:physics/0401008
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Abstract: The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.
30 January 2004.
Multipole interaction between atoms and their photonic environment
M. Wubs, L. G. Suttorp, and A. Lagendijk
Physical Review A 68, 013822 (2003)
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ArXiv:quant-ph/0307031
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Abstract: Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular, the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.
28 July 2003.
Quantum optics and multiple scattering in dielectrics
Martijn Wubs
PhD thesis, University of Amsterdam (2003). ISBN: 90-9016950-4
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11 June 2003.
Local optical densities of states in finite crystals of plane scatterers
M. Wubs and A. Lagendijk
Physical Review E 65, 046612 (2002)
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Abstract: Spontaneous emission rates in a dielectric structure are position dependent and proportional to the local optical density of states. The latter can be calculated when the Green function is known. In our scalar formalism, we model dielectric slabs as infinitely thin planes and use the T-matrix formalism of multiple-scattering theory to find an exact analytical expression for the Green function of a dielectric mirror of arbitrary number of unit cells N. All the propagating and guided modes of the structure are found. There are at most N guided modes and their dispersion relations are studied. The guided modes appear around frequencies corresponding to the first stop band in normal direction. Local densities of propagating and guided modes are presented, also for frequencies where the layered structure acts as an omnidirectional mirror.
2 April 2002.
Transient QED effects in absorbing dielectrics
M. Wubs and L. G. Suttorp
Physical Review A 63, 043809 (2001)
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ArXiv:quant-ph/0101075
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Abstract: The spontaneous-emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper, we consider the associated relaxation effects of the spontaneous-decay rate of atoms in dispersive and absorbing dielectric media for atomic-transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators at an initial time. The consistency of these solutions for the field and matter operators are found to depend on the validity of certain velocity sum rules. The transient effects in the spontaneous-decay rate are studied with the help of several specific models for the dielectric constant, which are shown to follow from the general theory by adopting particular forms of the bath coupling constant.
14 March 2001.
Exchange narrowing in dynamically disordered molecular aggregates
M. Wubs and J. Knoester
Chemical Physics Letters 284, 63 (1998)
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Abstract: We study the absorption lineshape for one-dimensional molecular aggregates with colored dynamic disorder. We show that exchange narrowing of the absorption spectrum, which is well-known in the limit of static disorder, also occurs for fast fluctuations, provided the fluctuation rate lambda is not large compared to the intermolecular excitation transfer interaction J. For small aggregates, the narrowing factor is found to equal the number of molecules in the aggregate, while for large aggregates it saturates at Sqrt(8 J / lambda) for lambda / J much smaller than 4. These results are derived for dichotomic noise, but we argue that they also hold in the fast-fluctuation limit of other Markov processes.
20 February 1998.
Optical absorption of molecular aggregates with colored noise
M. Wubs and J. Knoester
J. Lumin. 76-77, 359 (1998)
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Abstract: We study the optical absorption line shape for molecular aggregates in which the effect of the environment is modeled by a stochastic fluctuation of the molecular transition frequencies. We argue that exchange narrowing of this disorder is not only possible in the static limit, but also in the fast-fluctuation limit. The latter is further investigated using numerical calculations for dichotomic noise.
1998.
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