We develop a many-body theory for the properties of exciton-polaritons interacting strongly with a Bose-Einstein condensate (BEC) of exciton-polaritons in another spin state. Interactions lead to the presence of a two-body bound state, the bi-exciton, giving rise to a Feshbach resonance in the polariton spectrum when its energy is equal to that of two free polaritons. Using the minimal set of terms to describe this resonance, our theory recovers the main findings of two experiments probing interaction effects for upper and lower polaritons in a BEC. This strongly supports that Feshbach physics has indeed been realized, and we furthermore extract the energy and decay of biexciton from the experimental data. The decay rate is predicted to be much larger than that coming from its dissociation into two free polaritons indicating that other decay channels are important.
We examine the photoluminescence of highly-excited exciton-polariton condensates in semiconductor microcavities. Under strong pumping, exciton-polariton condensates have been observed to undergo a lasing transition where strong coupling between the excitons and photons is lost. We discuss an alternative high-density scenario, where the strong coupling is maintained. We find that the photoluminescence smoothly transitions between the lower polariton energy to the cavity photon energy. An intuitive understanding of the change in spectral characteristics is given, as well as differences to the ph…
We investigate the process of condensation of exciton-polaritons in a one-dimensional nanowire, predicting spontaneous formation of domains of uncondensed excitons and condensed polaritons. We demonstrate a universal scaling law for the density of domains, which results from the competition between characteristic timescales present in the system. However, we find that the system does not follow the standard Kibble-Żurek scenario of a nonequilibrium phase transition.
We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the…
We provide a many-body theory for the interactions of two-dimensional excitons and polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the two-body interaction strength in two-dimensions has an inverse logarithmic dependence on the scattering length and ground state energy. This leads to a vanishing exciton interaction strength in the zero-momentum limit but a finite polariton interaction strength due to strong light-matter coupling. We also derive the exact Tan relations for exciton-polaritons and calculate Tan's …
We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak dis- tributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot n…
Collective (elementary) excitations of quantum bosonic condensates, including condensates of exciton polaritons in semiconductor microcavities, are a sensitive probe of interparticle interactions. In anisotropic microcavities with momentum-dependent TE-TM splitting of the optical modes, the excitations dispersions are predicted to be strongly anisotropic, which is a consequence of the synthetic magnetic gauge field of the cavity, as well as the interplay between different interaction strengths for polaritons in the singlet and triplet spin configurations. Here, by directly measuring the disper…
Atomically-thin transition metal dichalcogenide crystals (TMDCs) hold great promise for future semiconductor optoelectronics due to their unique electronic and optical properties. In particular, electron-hole pairs (excitons) in TMDCs are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, the excitons can hybridise with cavity photons to form exciton polaritons (polaritons herein), which display both ultrafast velocities and strong interactions. The ability to manipulate and trap polaritons on a microchip is critical for future appli…
The dynamics of an exciton-polariton superfluid resonantly pumped in a semiconductor microcavity are investigated by mean-field theory. Modulational instability develops into crystalline order and then ordered and disordered states alternately form. A supersolid-like state is also found, in which superflow coexists with crystalline order at rest.
A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge--Kutta method of 4th order, fu…
We investigate the possibility of creating X-waves, or localized wave packets, in resonantly excited exciton-polariton superfluids. We demonstrate the existence of X-wave traveling solutions in the coupled exciton-photon system past the inflection point, where the effective mass of lower polaritons is negative in the direction perpendicular to the wavevector of the pumping beam. Contrary to the case of bright solitons, X-waves do not require nonlinearity for sustaining their shape. Nevertheless, we show that nonlinearity is important for their dynamics, as it allows for their spontaneous forma…
We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and excitons states in the polariton system without any oscillations of the phases of the two sub-condensates, we demonstrate that any non-zero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the tw…
Time resolved photoluminescence is a powerful technique to study the collective dynamics of excitons and polaritons in semiconductor nanostructures. We present a two excitation pulses technique to induce the ultrafast and controlled quenching of the exciton emission in a quantum well. The depth of the dip is given by the magnitude of the warming of the carriers induced by the arrival of a laser pulse when an exciton population is already present in the sample. We use this technique to study the relaxation mechanisms of polaritons in semiconductor microcavities, which are of great importance to…
We examine the Bose-Einstein condensation of exciton-polaritons in a semiconductor microcavity via an electrical current. We propose that by embedding a quantum dot p-i-n junction inside the cavity, the tunneling current through the device can reveal features of condensation due to a one-to-one correspondence of the photons to the condensate polaritons. Such a device can also be used to observe the phase interference of the order parameters from two condensates.
Strong light matter coupling between excitons and microcavity photons, as described in the framework of cavity quantum electrodynamics, leads to the hybridization of light and matter excitations. The regime of collective strong coupling arises, when various excitations from different host media are strongly coupled to the same optical resonance. This leads to a well-controllable admixture of various matter components in three hybrid polariton modes. Here, we study a cavity device with four embedded GaAs quantum wells hosting excitons that are spectrally matched to the A-valley exciton resonanc…
The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wavefunction approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit h…
Self-rotation occurs in an exciton-polariton condensate in a two-dimensional semiconductor microcavity pumped by a nonresonant Gaussian laser beam. A wave packet of the condensate spontaneously rotates around the center of the pumped region at a constant frequency breaking the rotation symmetry of the system. When two self-rotating condensates are created with an appropriate distance, synchronization occurs between the dynamics of the self-rotating condensates.
Exciton-polariton condensates are considered as a deterministic source of bright, coherent non-Gaussian light. Exciton-polariton condensates emit coherent light via the photoluminescence through the microcavity mirrors due to the spontaneous formation of coherence. Unlike conventional lasers which emit coherent Gaussian light, polaritons possess a natural nonlinearity due to the interaction of the excitonic component. This produces light with a negative component to the Wigner function at steady-state operation when the phase is stabilized via a suitable method such as injection locking. In co…
We theoretically study two-dimensional exciton-polariton lattices and predict that non-Hermitian topological corner modes can be formed under non-resonant pumping. As a generalization of the non-Hermitian skin effect, all eigenstates are localized at the two corners in our model. This is also a higher dimensional topology compared to other proposals in exciton-polariton systems and we find that it allows propagating signals in the bulk of the system to travel around defects, which is not possible in one-dimensional topological lattices or two-dimensional lattices with Hermitian edge states. Fu…
Diabolical points (degeneracies) can naturally occur in spectra of two-dimensional quantum systems and classical wave resonators due to simple symmetries. Geometric Berry phase is associated with these spectral degeneracies. Here, we demonstrate a diabolical point and the corresponding Berry phase in the spectrum of hybrid light-matter quasiparticles -- exciton-polaritons in semiconductor microcavities. It is well known that sufficiently strong optical pumping can drive exciton-polaritons to quantum degeneracy, whereby they form a macroscopically populated quantum coherent state similar to a B…
Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the THz frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic medium, the transition between both polaritonic states is dipole forbidden. In this work we show that in Cadmium Telluride microcavities, the Rabi-oscillation driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance conditi…
The transport distance of excitons in exciton-polariton systems has previously been assumed to be very small ($\lesssim 1~μ$m). The sharp spatial profiles observed when generating polaritons by non-resonant optical excitation show that this assumption is generally true. In this paper, however, we show that the transport distances of excitons in two-dimensional planar cavity structures with even a slightly polaritonic character are much longer than expected ($\approx 20~μ$m). Although this population of slightly polaritonic excitons is normally small compared to the total population of excitons…
We propose a method to enhance the spatial coupling between ballistic exciton-polariton condensates in a semiconductor microcavity based on available spatial light modulator technologies. Our method, verified by numerically solving a generalized Gross-Pitaevskii model, exploits the strong nonequilibrium nature of exciton-polariton condensation driven by localized nonresonant optical excitation. Tailoring the excitation beam profile from a Gaussian into a polygonal shape results in refracted and focused radial streams of outflowing polaritons from the excited condensate which can be directed to…
Dynamics of exciton-polariton multistability is theoretically investigated. Phase portraits are used as a tool to enlighten the microscopic phenomena which influence spin multistability of a confined polariton field as well as ultrafast reversible spin switching. The formation of a non-radiative reservoir, due to polariton pairing into biexcitons is found to play the lead role in the previously reported spin switching experiments. Ways to tailor this reservoir formation are discussed in order to obtain optimal spin switching reliability.
We report the formation of a macroscopic coherent state emerging from colliding polariton fluids. Four lasers with random relative phases, arranged in a square, pump resonantly a planar microcavity, creating four coherent polariton fluids propagating toward each other. When the density (interactions) increases, the four fluids synchronise and the topological excitations (vortex or soliton) disappear to form a single superfluid.
A quantum simulator is a purposeful quantum machine that can address complex quantum problems in a controllable setting and an efficient manner. This chapter introduces a solid-state quantum simulator platform based on exciton-polaritons, which are hybrid light-matter quantum quasi-particles. We describe the physical realization of an exciton-polariton quantum simulator in semiconductor materials (hardware) and discuss a class of problems, which the exciton-polariton quantum simulators can address well (software). A current status of the experimental progress in building the quantum machine is…
We observe quasi-long range coherence in a two-dimensional condensate of exciton-polaritons. Our measurements are the first to confirm that the spatial correlation algebraically decays with a slow power-law, whose exponent quantitatively behaves as predicted by the Berezinskii-Kosterlitz-Thouless theory. The exciton-polaritons are created by non-resonant optical pumping of a micro-cavity sample with embedded GaAs quantum-wells at liquid helium temperature. Michelson interference is used to measure the coherence of the photons emitted by decaying exciton-polaritons.
We analyze theoretically the role of the exciton-phonon interactions in phenomena related to the Josephson effect between two spatially separated exciton and exciton-polariton condensates. We consider the role of the dephasing introduced by phonons in such phenomena as Josephson tunneling, self-trapping and spontaneous polarization separation. In the regime of cw pumping we find a remarkable bistability effect arising from exciton- exciton interactions as well as regimes of self- sustained regular and chaotic oscillations.
We describe oblique half-solitons, a new type of topological defects in a two dimensional spinor Bose Einstein condensate. A realistic protocol based on the optical spin Hall effect is proposed toward their generation within an exciton-polariton system.
Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (i.e., non-Hermitian) quantum system: it requires constant pumping of energy and continuously decays releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and los…
Recently a new type of system exhibiting spontaneous coherence has emerged -- the exciton-polariton condensate. Exciton-polaritons (or polaritons for short) are bosonic quasiparticles that exist inside semiconductor microcavities, consisting of a superposition of an exciton and a cavity photon. Above a threshold density the polaritons macroscopically occupy the same quantum state, forming a condensate. The lifetime of the polaritons are typically comparable to or shorter than thermalization times, making them possess an inherently non-equilibrium nature. Nevertheless, they display many of the …
Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an optically-induced "box" trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and i…
We demonstrate the existence of the excited state of an exciton-polariton in a semiconductor microcavity. The strong coupling of the quantum well heavy-hole exciton in an excited 2s state to the cavity photon is observed in non-zero magnetic field due to surprisingly fast increase of Rabi energy of the 2s exciton-polariton in magnetic field. This effect is explained by a strong modification of the wave-function of the relative electron-hole motion for the 2s exciton state.
Exciton-polaritons (polaritons herein) offer a unique nonlinear platform for studies of collective macroscopic quantum phenomena in a solid state system. Shaping of polariton flow and polariton confinement via potential landscapes created by nonresonant optical pumping has gained considerable attention due to the degree of flexibility and control offered by optically-induced potentials. Recently, large density-dependent energy shifts (blueshifts) exhibited by optically trapped polaritons at low densities, below the bosonic condensation threshold, were interpreted as an evidence of strong polar…
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic pha…
We study the dynamics of exciton-polaritons in a double-well configuration. The system consists of two weakly coupled Bose-Josephson junctions, each corresponding to a different circular polarization of the polaritons, forming a {\it Josephson double dimer}. We show that the Josephson oscillation between the wells is strongly coupled to the polarization rotation and that consequently Josephson excitation is periodically exchanged between the two polarizations. Linearized analysis agrees well with numerical simulations using typical experimental parameters.
A Bose--Einstein condensate of exciton polaritons coexisting with a Fermi gas of electrons has been recently proposed as a promising system for realisation of room-temperature superconductivity [Phys. Rev. Lett., 104, 106402 (2010)]. In order to find the optimum conditions for exciton and exciton-polariton mediated superconductivity, we study the attractive mechanism between electrons of a Cooper pair mediated by the exciton and exciton-polariton condensate and analyze the gap equation that follows. We specifically address microcavities with embedded n-doped quantum wells as well as coupled qu…
Optical trapping and manipulation of microcavity exciton polaritons rely on effective potentials induced by the interaction of polaritons with a reservoir of high energy excitonic particles injected by an off-resonant optical pump. Here, we experimentally investigate possible mechanisms responsible for reshaping of these effective potentials in the low-density exciton-polariton regime. We infer the spatial distribution of the reservoir from the spatially resolved energy of exciton-polariton emission measured at zero momentum (zero kinetic energy). Power-dependent shape analysis of the potentia…
We address stationary patterns in exciton-polariton condensates supported by a narrow external pump beam, and we discover that even in the absence of trapping potentials, such condensates may support stable localized stationary dissipative solutions (quasi-compactons), whose field decays faster than exponentially or even vanishes everywhere outside the pump spot. More general conditions lead to dissipative solitons which may display bistability. The bistability in exciton-polariton condensates, which manifests itself in simultaneous existence of two stable and one unstable localized solitons w…
Exciton-polaritons are a coherent electron-hole-photon (e-h-p) system where condensation has been observed in semiconductor microcavities. In contrast to equilibrium Bose-Einstein condensation (BEC) for long lifetime systems, polariton condensates have a dynamical nonequilibrium feature owing to the similar physical structure that they have to semiconductor lasers. One of the distinguishing features of a condensate to a laser is the presence of strong coupling between the matter and photon fields. Irrespective of its equilibrium or nonequilibrium nature, exciton-polariton have been observed to…
We study nonresonantly pumped exciton-polariton system in the vicinity of the dynamical instability threshold. We find that the system exhibits unique and rich dynamics, which leads to spatiotemporal pattern formation. The patterns have a tree-like structure and are reminiscent of structures that appear in a variety of soft matter systems. Within the approximation of slow and fast time scales, we show that the polariton model exhibits self-replication point in analogy to reaction-diffusion systems.
Equilibrium Bose-Einstein condensation of exciton-polaritons, demonstrated with a long-lifetime microcavity [Phys. Rev. Lett. 118, 016602 (2017)], has proven that driven-dissipative systems can undergo thermodynamic phase transitions in the limit where the quasiparticle lifetime exceeds the thermalization time. Here, we identify the role of dimensionality and polariton interactions in determining the degree of thermalization in optically generated traps. To distinguish the effect of trapping from interactions and lifetimes, we measured the polariton distribution under four nonresonant Gaussian…
Spin-orbit coupling (SOC) is responsible for a range of spintronic and topological processes in condensed matter. Here we show photonic analogs of SOCs in exciton-polaritons and their condensates in microcavities composed of birefringent lead halide perovskite single crystals. The presence of crystalline anisotropy coupled with splitting in the optical cavity of the transverse electric (TE) and transverse magnetic (TM) modes gives rise to a non-Abelian gauge field, which can be described by the Rashba-Dresselhaus Hamiltonian near the degenerate points of the two polarization modes. With increa…
We resonantly excite exciton-polariton states confined in cylindrical traps. Using a homodyne detection setup, we are able to image the phase and amplitude of the confined polariton states. We evidence the excitation of vortex states, carrying an integer angular orbital momentum m, analogous to the transverse TEM01* "donut" mode of cylindrically symmetric optical resonators. Tuning the excitation conditions allows us to select the charge of the vortex. In this way, the injection of singly charged (m = 1 & m = -1) and doubly charged (m = 2) polariton vortices is shown. This work demonstrates th…
We present numerical analysis of steady states in a two-component (spinor) driven-dissipative quantum fluid formed by condensed exciton-polaritons in an annular optically induced trap. We demonstrate that an incoherent ring-shaped optical pump creating the exciton-polariton confinement supports the existence of stationary and rotating azimuthon steady states with azimuthally modulated density. Such states can be imprinted by coherent light pulses with a defined orbital angular momentum, as well as generated spontaneously in the presence of thermal noise.
We show that in a non-equilibrium system of an exciton-polariton condensate, where polaritons are generated from incoherent pumping, a ring-shaped pump allows for stationary vortex memory elements of topological charge $m = 1$ or $m = -1$. Using simple potential guides we can choose whether to copy the same charge or invert it onto another spatially separate ring pump. Such manipulation of binary information opens the possibility of a new type processing using vortices as topologically protected memory components.
We report on time resolved measurements of the first order spatial coherence in an exciton polariton Bose-Einstein condensate. Long range spatial coherence is found to set in right at the onset of stimulated scattering, on a picosecond time scale. The coherence reaches its maximum value after the population and decays slower, staying up to a few hundreds of picoseconds. This behavior can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential.
