We present a fully microscopic approach to the transition rate of two exciton-photon polaritons. The non-trivial consequences of the polariton composite nature -- here treated exactly through a development of our composite-exciton many-body theory -- lead to results noticeably different from the ones of the conventional approaches in which polaritons are mapped into elementary bosons. Our work reveals an appealing fundamental scattering which corresponds to a photon-assisted exchange -- in the absence of Coulomb process. This scattering being dominant when one of the scattered polaritons has a strong photon character, it should be directly accessible to experiment. In the case of microcavity polaritons, it produces a significant enhancement of the polariton transition rate when compared to the one coming from Coulomb interaction. This paper also contains the crucial tools to securely tackle the many-body physics of polaritons, in particular towards its possible BEC.
Using the Feynman-Dyson diagram technique, we study nonlinear polariton-polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with subs…
We report on confined exciton resonances of acoustic and folded acoustic phonon light scattering in a GaAs/AlAs multi-quantum-well. Significant variations of the line shifts and widths are observed across the resonance and quantitatively reproduced in terms of the polariton dispersion. This high resolution Brillouin study brings new unexpectedly detailed informations on the polariton dynamics in confined systems.
Polariton lasing has recently been observed in strongly coupled crystalline anthracene microcavities. A simple model is developed describing the onset of the non-linear threshold based on a master equation including the relevant relaxation processes and employing realistic material parameters. The mechanism governing the build-up of the polariton population - namely bosonic stimulated scattering from the exciton reservoir via a vibronically assisted process - is characterized and its efficiency calculated on the basis of a microscopic theory. The role of polariton-polariton bimolecular quenchi…
The resonant scattering of surface plasmon-polariton waves by embedded semiconductor quantum dots above the dielectric/metal interface is explored in the strong-coupling regime. In contrast to non-resonant scattering by a localized dielectric surface defect, a strong resonant peak in the scattering field spectrum is predicted and accompanied by two side valleys. The peak height depends nonlinearly on the amplitude of surface plasmon-polariton waves, reflecting the feedback dynamics from a photon-dressed electron-hole plasma inside the quantum dots. This unique behavior in the scattering field …
A signature of the scattering between microcavity polaritons and longitudinal optical phonons has been observed in the electroluminescence spectrum of an intersubband device operating in the light-matter strong coupling regime. By electrical pumping we resonantly populate the upper polariton branch at different energies as a function of the applied bias. The electroluminescent signal arising from these states is seconded by a phonon replica from the lower branch.
The plasmon and phonon polaritons of two-dimensional (2d) and van-der-Waals materials have recently gained substantial interest. Unfortunately, they are notoriously hard to observe in linear response because of their strong confinement, low frequency and longitudinal mode symmetry. Here, we propose a fundamentally new approach of harnessing nonlinear resonant scattering that we call stimulated plasmon polariton scattering (SPPS) in analogy to the opto-acoustic stimulated Brillouin scattering (SBS). We show that SPS allows to excite, amplify and detect 2d plasmon and phonon polaritons all acros…
We study a "strongly-coupled" (SC) polariton system formed between the atom-like intersubband transitions in a semiconductor nanostructure and the THz optical modes that are localised at the edges of a gold aperture. The polaritons can be excited optically, by incoherent excitation with bandgap radiation, and we find that they also coherently scatter the same input laser, to give strikingly sharp "sideband" (SB) spectral peaks in the backscattered spectrum. The SB intensity is a sensitive track of the polariton density and they can be detected down to a quantum noise floor that is more than 25…
We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an ad…
We theoretically calculate the polariton linewidth associated with the polariton-electron scattering in a microcavity in presence of a magnetic field perpendicular to the microcavity plane. It is shown that the polariton linewidth oscillates as a function of the magnetic field magnitude and the polariton-electron scattering rate can be not only decreased but also increased by the magnetic field. The possible applications of such an effect are discussed.
New techniques for probing hyperbolic phonon polaritons (HPP) in 2D materials will support the development of the emerging technologies in this field. Previous reports have shown that it is possible for WSe2 monolayers in contact with the hexagonal boron nitride (hBN) to generate HPP in the hBN via Raman scattering. In this paper, we set out new results on HPP Raman scattering induced in hBN by WSe2 and MoSe2 monolayers including new resonances at which the Raman scattering is enhanced. Analysis of the observed Raman lineshapes demonstrates that Raman scattering allows HPP with wavevectors wit…
We report experimental evidence of longitudinal optical (LO) phonon-intersubband polariton scattering processes under resonant injection of light. The scattering process is resonant with both the initial (upper polariton) and final (lower polariton) states and is induced by the interaction of confined electrons with longitudinal optical phonons. The system is optically pumped with a mid-IR laser tuned between 1094 cm-1 and 1134 cm-1 (lambda=9.14 um and lambda=8.82 um). The demonstration is provided for both GaAs/AlGaAs and InGaAs/AlInAs doped quantum well systems whose intersubband plasmon lie…
The ultrafast scattering dynamics of intersubband polaritons in dispersive cavities embedding GaAs/AlGaAs quantum wells are studied directly within their band structure using a non-collinear pump-probe geometry with phase-stable mid-infrared pulses. Selective excitation of the lower polariton at a frequency of ~25 THz and at a finite in-plane momentum, $k_{||}$, leads to the emergence of a narrowband maximum in the probe reflectivity at $k_{||}=0$. A quantum mechanical model identifies the underlying microscopic process as stimulated coherent polariton-polariton scattering. These results mark …
We report observation of coherent oscillations in the relaxation dynamics of an exciton-polariton condensate driven by parametric scattering processes. As a result of the interbranch scattering scheme and the nonlinear polariton-polariton interactions, such parametric scatterings exhibit high scattering efficiency, which leads to fast depletion of the polariton condensate and periodic shut-off of the bosonic stimulation processes, eventually causing relaxation oscillations. Employing polariton-reservoir interactions, the oscillation dynamics in the time domain can be projected onto the energy …
We investigate and compare different optical probes of a condensed state of microcavity polaritons in expected experimental conditions of non-resonant pumping. We show that the energy- and momentum-resolved resonant Rayleigh signal provide a distinctive probe of condensation as compared to, e.g., photoluminescence emission. In particular, the presence of a collective sound mode both above and below the chemical potential can be observed, as well as features directly related to the density of states of particle-hole like excitations. Both resonant Rayleigh response and the absorption and photol…
We have performed real and momentum space spin-dependent spectroscopy of spontaneously formed exciton polariton condensates for a non-resonant pumping scheme. Under linearly polarized pump, our results can be understood in terms of spin-dependent Boltzmann equations in a two-state model. This suggests that relaxation into the ground state occurs after multiple phonon scattering events and only one polariton-polariton scattering. For the circular pumping case, in which only excitons of one spin are injected, a bottleneck effect is observed, implying inefficient relaxation.
A scheme is proposed for the generation of branch-entangled pairs of microcavity polaritons through spontaneous inter-branch parametric scattering. Branch-entanglement is achievable when there are two twin processes, where the role of signal and idler can be exchanged between two different polariton branches. Branch-entanglement of polariton pairs can lead to the emission of frequency-entangled photon pairs out of the microcavity. In planar microcavities, the necessary phase-matching conditions are fulfilled for pumping of the upper polariton branch at an arbitrary in-plane wave-vector. The im…
Electric dipole transitions between different cavity polariton branches or between dressed atomic states with the same excitation number are strictly forbidden in centro-symmetric systems. For doped quantum wells in semiconductor microcavities, the strong coupling between an intersubband transition in the conduction band and a cavity mode produces two branches of intersubband cavity polaritons, whose normal-mode energy splitting is tunable and can be in the terahertz region. Here, we show that, by using asymmetric quantum wells, it is possible to have allowed dipolar transitions between differ…
Plexciton-mediated Raman scattering in strongly coupled systems
Institute of Light Resources and Environmental Science, Henan Academy of Sciences（河南省科学院光资源与环境科学研究所）；School of Physics, Xi’an Jiaotong University（西安交通大学物理学院）
We provide an analytical solution to the problem of scattering of electromagnetic radiation by a square-wave grating with a flat graphene sheet on top. We show that for deep groves there is a strong plasmonic response with light absorption in the graphene sheet reaching more than 45%, due to the excitation of surface plasmon-polaritons. The case of grating with a graphene sheet presenting an induced periodic modulation of the conductivity is also discussed.
We theoretically investigate the nonlinearity of trion-polaritons in a two-dimensional material that arises from Coulomb interaction between quasiparticles. To evaluate the interaction constant, we solve a three-body Wannier equation precisely by expanding trion wavefunctions into a Gaussian basis. Using these wavefunctions, we calculate the trion-polariton interaction energies for the exchange processes, resolving the outstanding question of trion-trion scattering. We find that the nonlinearity is the result of the competition between different scattering channels. Such a cancellation effect …
Recent experiments in exciton-polariton systems have provided high-precision measurements of the value of the polariton-polariton interaction constant, which is a key parameter that governs the nonlinear dynamics of polariton condensates and potentially enables quantum correlated polaritons. Yet, until now, this parameter has only been addressed theoretically using perturbative treatments or approximations that do not include the composite nature of the excitons. Here, we use a recently developed microscopic description of polaritons involving electrons, holes, and photons, where the interacti…
Based on the semiclassical model Hamiltonian of the surface plasmon polariton and the nonequilibrium Green-function approach, we present a microscopic kinetic theory to study the influence of the electron scattering on the dynamics of the surface plasmon polariton in semiconductor nanowires. The damping of the surface plasmon polariton originates from the resonant absorption by the electrons (Landau damping), and the corresponding damping exhibits size-dependent oscillations and distinct temperature dependence without any scattering. The scattering influences the damping by introducing a broad…
We investigate light-matter coupling in metallic crystals where plasmons coexist with phonons exhibiting large oscillator strength. We demonstrate theoretically that this coexistence can lead to strong light-matter interactions without external resonators. When the frequencies of plasmons and phonons are comparable, hybridization of these collective matter modes occurs in the crystal. We show that the coupling of these modes to photonic degrees of freedom gives rise to intrinsic surface plasmon-phonon polaritons, which offer the unique possibility to control the phonon properties by tuning the…
We consider scattering of surface plasmon polaritons (SPPs) and light by individual high-refractive-index dielectric nanoparticles (NPs) located on a metal (gold) substrate and supporting electric and magnetic dipole resonances in the visible spectral range. Numerical calculations are carried out by making use of the discrete dipole approximation including the multipole decomposition procedure. Extinction and scattering cross section spectra of spheroid silicon NPs in visible and near-infrared are presented and discussed. The roles of the in-plane and out-of-plane components of electric and ma…
We demonstrate theoretically that the interaction of two degenerate condensates of exciton-polaritons in microcavities leads to polarization dependent parametric oscillations. The resonant polariton-polariton scattering is governed by the polarization of the condensates and can be fully suppressed for certain polarizations. A polarization controlled solid state optical gate is proposed.
We study the TE polarized electromagnetic surface wave propagating along the interface between materials with positive and negative magnetic permeability. Contrary to the TM polarized surface wave, the TE surface wave exhibits almost no radiation losses when scattered at semi-infinite dielectric interfaces.
We present a detailed theoretical study of transverse exciton-polariton patterns in semiconductor quantum-well microcavities. These patterns are initiated by directional instabilities in the uniform pump-generated polariton field and are measured as optical patterns in a transverse plane in the far field. Based on a microscopic many-particle theory, we investigate the spatio-temporal dynamics of the formation, selection, and optical control of these patterns. An emphasis is placed on a previously proposed low-intensity, all-optical switching scheme designed to exploit these instability-driven …
We study the kinetics of polariton condensation accounting for the condensation process as well as the energy relaxation of condensed polaritons due to their scattering with phonons and excitons. By assuming a Boltzmann kinetic description of the scattering process, we show that intra-condensate relaxation can be accounted for by an additional time-dependent term in the Gross-Pitaevskii equation. As an example, we apply the formalism to the experimental results recently obtained in polariton microwires [E. Wertz, et al., Nature Phys. 6, 860 (2010)]. In the presence of a local non-resonant opti…
We present a generic model for the description of non-equilibrium Bose-Einstein condensates, suited for the modelling of non-resonantly pumped polariton condensates in a semiconductor microcavity. The excitation spectrum and scattering of the non-equilibrium condensate with a defect are discussed.
We show that when a monopolar current is passed through an n-i-n structure, superlinear photocurrent response occurs when there is a polariton condensate. This is in sharp contrast to the previously observed behavior for a standard semiconductor laser. Theoretical modeling shows that this is due to a stimulated exciton-exciton scattering process in which one exciton relaxes into the condensate, while another one dissociates into an electron-hole pair.
The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the scattering at an interface where there is a sudden change of the electronic doping. The formalism is then extended to the {\it barrier problem}. In this system rich physics is found for the plasmonic mode, showing: total reflection, total transmission, Fabry-Pérot oscillations, and coupling to photonic modes.
We study the effects of imprinting a single-quantized vortex on the steady state of a microcavity exciton-polariton condensate generated via parametric scattering. Interestingly we observe two distinct regimes: In the first case, at low polariton densities, the effect of the pulsed probe, containing the vortex state, is to generate a gain response in the condensate lasting for tens of picoseconds during which no dissipation of the circulating currents is detected. In the second regime, at higher densities, the gain lasts much less and the circulation is imprinted directly into the steady state…
We introduce and model spin-Rabi oscillations based on exciton-polaritons in semiconductor microcavities. The phase and polarization of oscillations can be controlled by resonant coherent pulses and the propagation of oscillating domains gives rise to phase-dependent interference patterns in real space. We show that interbranch polariton-polariton scattering controls the propagation of oscillating domains, which can be used to realize logic gates based on an analogue variable phase.
Within the framework of the mean-field approximation, a coherently excited two-dimensional system of weakly repulsive bosons is predicted to show a giant loop scattering when the rotational symmetry is reduced. The considered process combines (i) the parametric decay of the driven condensate into different k-states and (ii) their massive back scattering owing to spontaneous synchronization of several four-wave mixing channels. The hybridization of the direct and inverse scattering processes, which are different and thus do not balance each other, makes the condensate oscillate under constant o…
Strong coupling between cavity photons and molecular vibrations can lead to the formation of vibron-polaritons. In a recent experiment with PVAc molecules in a metal-metal microcavity [A.Shalabney et al., Ang.Chem.Int.Ed. 54 7971 (2015)], such a coupling was observed to enhance the Raman scattering probability by several orders of magnitude. Inspired by this, we theoretically analyze the effect of strong photon-vibron coupling on the Raman scattering amplitude of organic molecules. This problem has recently been addressed in [J.del Pino, J.Feist and F.J.Garcia-Vidal; J.Phys.Chem.C 119 29132 (2…
We present theoretical and experimental study of resonant Brillouin scattering of excitonic polaritons in one-dimensional multiple-quantum-well structure. We obtain general analytical results for the scattering light spectra, valid for arbitrary quantum well arrangement. Application of our theory to the specific case of short-period superlattice shows a perfect quantitative agreement with experimental results for the height, width and position of the Brillouin scattering peaks and allows us to determine the energy, radiative and nonradiative decay rates of quantum well excitons. We reveal the …
Two dimensional semiconductors provide an ideal platform for exploration of linear exciton and polariton physics, primarily due to large exciton binding energy and strong light-matter coupling. These features, however, generically imply reduced exciton-exciton interactions, hindering the realisation of active optical devices such as lasers or parametric oscillators. Here, we show that electrical injection of itinerant electrons into monolayer molybdenum diselenide allows us to overcome this limitation: dynamical screening of exciton-polaritons by electrons leads to the formation of new quasi-p…
We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory - which is fundamentally different from the analogous photonic scenario - is used to investigate the possibility of plasmonic beamsplitters at the quantum level. Remarkably, we find that a wide-range of splitting ratios can be reached. As an application, we characterize a 50:50 plasmonic beamsplitter and investigate first-order quantum interference of surface plasmon polaritons. The results of this theoretical study show that surface plasmon beamsplitters are ab…
Spontaneous Raman Scattering under Vibrational Strong Coupling: The Critical Role of Polariton Spatial Mode Coherence
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡大学）；Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学）
Recently the possibility of generating nonclassical polariton states by means of parametric scattering has been demonstrated. Excitonic polaritons propagate in a complex interacting environment and contain real electronic excitations subject to scattering events and noise affecting quantum coherence and entanglement. Here we present a general theoretical framework for the realistic investigation of polariton quantum correlations in the presence of coherent and incoherent interaction processes. The proposed theoretical approach is based on the {\em nonequilibrium quantum Langevin approach for o…
We calculate the dispersion of spinor exciton-polaritons in a planar microcavity with its active region containing a single Transitional Metal Dichalcogenide (TMD) monolayer, taking into account excitonic and photonic spin-orbit coupling. We consider the radial propagation of polaritons in presence of disorder. We show that the reduction of the disorder scattering induced by the formation of polariton states allows to observe an optical Valley Hall effect, namely the coherent precession of the locked valley and polarization pseudospins leading to the formation of spatial valley-polarized domai…
Third order anharmonic scattering in light-matter systems can drive a wide variety of practical and physically interesting processes from lasing to polariton condensation. Motivated by recent experimental results in the nonlinear optics of localised phonon polaritons, in this Letter we develop a quantum theory capable of describing four-wave mixing in arbitrarily inhomogeneous photonic environments. Using it we investigate Kerr self-interaction and parametric scattering of surface and localised phonon polaritons, showing both processes to be within experimental reach.
The interplay between strong light-matter interactions and charge doping represents an important frontier in the pursuit of exotic many-body physics and optoelectronics. Here, we consider a simplified model of a two-dimensional semiconductor embedded in a microcavity, where the interactions between electrons and holes are strongly screened, allowing us to develop a diagrammatic formalism for this system with an analytic expression for the exciton-polariton propagator. We apply this to the scattering of spin-polarized polaritons and electrons, and show that this is strongly enhanced compared wi…
We report on the formation of a diverse family of transverse spatial polygon patterns in a microcavity polariton fluid under coherent driving by a blue-detuned pump. Patterns emerge spontaneously as a result of energy-degenerate polariton-polariton scattering from the pump state to interfering high order vortex and antivortex modes, breaking azimuthal symmetry. The interplay between a multimode parametric instability and intrinsic optical bistability leads to a sharp spike in the value of second order coherence $g^{(2)}(0)$ of the emitted light, which we attribute to the strongly superlinear k…
We explore nonlinear transitions of polariton wavepackets, first, to a soliton and then to a standing wave polariton condensate in a multi-mode microwire system. At low polariton density we observe ballistic propagation of the multi-mode polariton wavepackets arising from the interference between different transverse modes. With increasing polariton density, the wavepackets transform into single mode bright solitons due to effects of both inter-modal and intra-modal polariton-polariton scattering. Further increase of the excitation density increases thermalisation speed leading to relaxation o…
The role of polariton-electron scattering on the performance characteristics of an electrically injected GaAs-based quantum well microcavity diode in the strong coupling regime has been investigated. An electron gas is introduced in the quantum wells by modulation doping with silicon dopants. It is observed that polariton-electron scattering suppresses the relaxation bottleneck in the lower polariton branch. However, it is not adequate to produce a degenerate coherent condensate at k|| ~ 0 and coherent emission.
The transport properties of exciton-polaritons are studied with allowance for their polarization. Both classical multiple scattering effects and quantum effects such as weak localization are taken into account in the framework of a generalized kinetic equation. The longitudinal-transverse (TE-TM) splitting of polariton states which plays role analogous to the spin-orbit splitting in electron systems is taken into account. The developed formalism is applied to calculate the particle and spin diffusion coefficients of exciton-polaritons, spin relaxation rates and the polarization conversion effi…
Terahertz emission between exciton-polariton branches in semiconductor microcavities is expected to be strongly stimulated in the polariton laser regime, due to the high density of particles in the lower state (final state stimulation effect). However, non-radiative scattering processes depopulate the upper state and greatly hinder the efficiency of such terahertz sources. In this work, we suggest a new scheme using multiple microcavities and exploiting the transition between two interband polariton branches located below the exciton level. We compare the non-radiative processes loss rates in …
The scattering of light and surface plasmon polaritons (SPPs) by finite arrays of either holes or dimples in a metal film is treated theoretically. A modal expansion formalism, capable of handling real metals with up to thousands of indentations, is presented. Computations based on this method demonstrate that a single hole scatters a significant fraction of incoming light into SPPs. It is also observed that holes and dimples scatter SPPs into light with similar efficiencies, provided the depth of the dimple is larger than its radius. Finally, it is shown that in arrays the normalized-to-area …
We study the thermodynamic condensation of microcavity polaritons using a realistic model of disorder in semiconductor quantum wells. This approach correctly describes the polariton inhomogeneous broadening in the low density limit, and treats scattering by disorder to all orders in the condensed regime. While the weak disorder changes the thermodynamic properties of the transition little, the effects of disorder in the condensed state are prominent in the excitations and can be seen in resonant Rayleigh scattering.
Exciton-photon beats known as polariton Rabi oscillations in semiconductor microcavities are usually excited by short pulses of light. We consider a different pumping scheme, assuming a cw pumping of the Rabi oscillator from an exciton reservoir. We account for the initial pulse of light setting the phase, exciton decay due to exciton-phonon and exciton-exciton scattering, photon leakage, and blueshift of the exciton resonance due to interactions. We find non-trivial stationary solutions reminiscent of Kapitza pendulum, where polaritons are accumulated at the upper branch while the lower branc…
Strong coupling between light and matter is possible with a variety of organic materials. In contrast to the simpler inorganic case, organic materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing, and if strong enough, can suppress the entanglement between electronic and vibrational degrees of freedom. By exploiting symmetries, we can perform exact numerical diagonalization to find the polaritonic states for intermediate numbers of molecules, and use these to define and validate accurate e…
Entanglement generation in microcavity exciton-polaritons is an interesting application of the peculiar properties of these half-light/half-matter quasiparticles. In this paper we theoretically investigate their luminescence dynamics and entanglement formation in single, double, and triple cavities. We derive general expressions and selection rules for polariton-polariton scattering. We evaluate a number of possible parametric scattering schemes in terms of entanglement, and identify the ones that are experimentally most promising.
