Pump Polaritons Research Articles

Resonantly enhanced polariton wave mixing and parametric instability in a Floquet medium.

We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear systems of optical phonons. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell's equations and leads to phenomena such as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. [Proc. Natl. Acad. Sci. U. S. A. 115, 12148 (2018)], which demonstrated light amplification in a resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.

Drag force of an exciton-polariton condensate under nonresonant pumping

Exciton-polariton condensate in semiconductor microcavities constitute a novel kind of non-equilibrium superfluid. In a recent experiment [P. Stepanov, {\it et. al.,} Nat. Commun. {\bf 10}, 1038 (2019)], the dispersion relation of collective excitations in a polariton condensate under the resonant pumping has been investigated with the emphasis on the role of reservoir of long-lived excitons in determining the superfluidity. Inspired by such an experimental advance, we study the superfluidity of a exciton-polaritonn condensate under non-resonant pumping by calculating the drag force exerted on a classical impurity moving in a polariton condensate. For a non-resonant pumped polariton condensate prepared in the gapped phase, due to the reservoir's modes, the drag force can be large when the velocity of the impurity is small. Besides, as the velocity increases, the drag force can decrease. For not very large velocity, the drag force is enhanced if the condensate is tuned to be more dissipative. When the condensate is close to the transition point between the gapped phase and the gapless one, the drag force is similar to that of the equilibrium superfluid. Our present work reveals the effects of the reservoir's modes on the superfluidity properties of a polariton condensate with the non-resonant pumping.

Nonlinear Dynamics of Parametric Oscillations of Exciton–Polaritons in a Semiconductor Microcavity

The polariton dynamics in a microcavity in the parametric oscillator mode is studied when two pump polaritons turn into polaritons of signal and idler modes and vice versa. The pumping is performed by two laser pulses with close frequencies. Analytical solutions to a system of nonlinear differential equations are obtained. Periodic and aperiodic regimes of transformation of a pair of pump polaritons into polaritons of signal and idler modes, as well as the quiescent mode of the system, are obtained.

Theory of relaxation oscillations in exciton-polariton condensates

We provide an analytical and numerical description of relaxation oscillations in the nonresonantly pumped polariton condensate. The presented considerations are based on the open dissipative Gross-Pitaevskii equation coupled to a pair of rate equations. The evolution of the condensate density can be explained qualitatively by studying the topology of the trajectory in phase space. We use a fixed points analysis for the classification of the different regimes of condensate dynamics, including fast stabilization, slow oscillations and ultrashort pulse emission. We obtain an analytical condition for the occurrence of relaxation oscillations. Continuous and pulsed condensate excitation considered and we demonstrate that in the latter case the existence of the second reservoir is necessary for the emergence of oscillations. We show that relaxation oscillations should be expected to occur in systems with relatively short polariton lifetime.

Nonlinear Dynamics of Parametric Oscillations of Polaritons in a Microcavity

The dynamics of polaritons in a microcavity in the parametric oscillator mode, when two pump polaritons turn into the signal and idler polaritons and vice versa, has been studied. The pumping is carried out using two lasers with close frequencies. Analytical solutions of the system of nonlinear differential equations have been obtained. The periodic and aperiodic modes of the transformation of a pair of pump polaritons into signal and idler polaritons have been found.

Matter wave coupling of spatially separated and unequally pumped polariton condensates

Spatial quantum coherence between two separated driven-dissipative polariton condensates created non-resonantly and with a different occupation is studied. We identify the regions where the condensates remain coherent with the phase difference continuously changing with the pumping imbalance and the regions where each condensate acquires its own chemical potential with phase differences exhibiting time-dependent oscillations. We show that in the mutual coherence limit the coupling consists of two competing contributions: a symmetric Heisenberg exchange and the Dzyloshinskii-Moriya asymmetric interactions that enable a continuous tuning of the phase relation across the dyad and derive analytic expressions for these types of interactions. The introduction of non-equal pumping increases the complexity of the type of the problems that can be solved by polariton condensates arranged in a graph configuration. If equally pumped polaritons condensates arrange their phases to solve the constrained quadratic minimisation problem with a real symmetric matrix, the non-equally pumped condensates solve that problem for a general Hermitian matrix.

Self-trapping phenomenon in exciton-polariton dynamics

The polariton dynamics in a microcavity in the parametric oscillator mode, when two pump polaritons are transformed into signal and idler polaritons and vice versa, has been studied. A nonlinear differential equation is obtained, which describes the temporal evolution of pump-polariton density, the solution of which is expressed in terms of the Jacobi elliptical functions. The amplitude and period of polaritondensity oscillations are determined by the initial polariton densities and the resonance detuning. The possibility of self-trapping in exciton-polariton dynamics is predicted.

Nonlinear dynamics of an optical parametric exciton-polariton oscillator in semiconductor microcavity

The dynamics of optical parametric exciton-polariton oscillations in semiconductor microcavities was studied, taking into account the conversion processes of the two pump polaritons into signal and idler polaritons and vice versa. The system of nonlinear evolution equations was obtained for describing the time evolution for the densities of pump, signal and idler polaritons. The periodic and aperiodic regimes of the evolution of polariton densities exist. The period and amplitude of oscillations of the polariton densities essentially depend on the initial densities of polaritons, initial phase difference and resonance detuning. For the definite relation between the parameters, the aperiodic evolution of the system is possible, too, representing the conversion of only part of the pump polaritons, which finishes the evolution of the system. The significant dependence of the period and amplitude of polariton oscillations on the initial phase difference is evidence of the possibility of the phase controlling of the polariton dynamics. The damping of the system of coherent polaritons leads to the oscillatory decay of polariton density in time, the rate of which is defined by the polariton damping constants.

Stability of nonequilibrium polariton superflow in the presence of a cylindrical defect

We make a theoretical study of the stability of nonequilibrium polariton superflows that interact with a cylindrical defect. The nonresonantly pumped polariton condensate is modeled with a generalized complex Ginzburg-Landau equation. At low pump intensities the dissipation is found to stabilize the superflow. At large pump intensities, we find an instability that sets a lower critical speed for superfluidity. For even larger pump power, the lower and upper critical speeds meet and stable superflows are no longer possible.

Dynamics of a parametric exciton-polariton oscillator in a microcavity

We study the dynamics of parametric oscillations of polaritons in a microcavity that consists of a periodic conversion of a pair of pump polaritons into polaritons of signal and idle modes and vice versa. The period and amplitude of oscillations considerably depend on the initial polariton density, the initial phase difference, and the resonance detuning. We show that there is a possibility of phase controlling the polariton dynamics in the microcavity.

Dynamics of an exciton-polariton parametric oscillator

The dynamics of an exciton-polariton parametric oscillator has been investigated. A system of nonlinear differential equations has been obtained for describing the time evolution of the densities of pump polaritons and polaritons of the signal mode. It has been demonstrated that, depending on the system parameters, the time evolution of the density of polaritons can occur in the periodic and aperiodic regimes, as well as at rest. The possibility of exercising phase control of the time evolution of the system has been proved.

Vortex Lattices in Coherently Pumped Polariton Microcavities

We propose a new class of vortex lattices supported by the parametric conversion of polaritons in wide aperture semiconductor microcavities operating in the strong coupling regime and pumped by a coherent beam. We present numerical and analytical results confirming the existence and robustness of the polaritonic vortex lattices in practically relevant settings and discuss their melting scenarios.

Quantum optics in semiconductor microcavities

AbstractPolaritons in semiconductor microcavities are hybrid quasiparticles consisting of a superposition of cavity photons and two‐dimensional excitons in embedded quantum wells (QWs). Owing to their exciton content, they have a strong mutual interaction which can be exploited for producing spontaneous parametric scattering of pump polaritons into signal‐idler polariton pairs. This process is able to produce polariton states exhibiting quantum correlations, and can thus be exploited for potential applications as well as to study quantum optical processes within a complex many‐body system. Here we present an overview of polariton parametric processes within a full quantum description based on the dynamics controlled truncation scheme. We also describe the results of an experiment that proves the existence of polariton pair correlations. This interpretation is confirmed by a microscopic theoretical analysis of the measured interference visibility. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Excitations and superfluidity in non-equilibrium Bose–Einstein condensates of exciton–polaritons

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.

Four Wave Mixing Oscillation in a Semiconductor Microcavity: Generation of Two Correlated Polariton Populations

We demonstrate a novel kind of polariton four wave mixing oscillation. Two pump polaritons scatter towards final states that emit two beams of equal intensity, separated both spatially and in polarization with respect to the pumps. The measurement of the intensity fluctuations of the emitted light demonstrates that the final states are strongly correlated.

Polarisation properties of optical parametric oscillator emission in a semiconductor microcavity

AbstractPolarisation properties of the light emitted by a semiconductor microcavity are studied in the regime of stimulated parametric scattering for one and two beam continuous wave excitation. For linearly polarized excitation with one beam we observe strongly linearly polarized signal emission with the plane of polarization rotated by 60°–120° relative to that of the pump. Moreover, a degree of circular polarisation is found for certain orientations of the plane of polarisation of the pump. These effects arise from the splitting between linearly and circularly polarized polariton states, as well as from the anisotropy of polariton‐polariton scattering. Resonantly exciting the lower polariton branch simultaneously with two independent cross circularly polarised pumps with opposite k‐vectors, we observe an enhancement of the total signal emission at k = 0 by 3–5 times, accompanied by a new idler state located at k = 0. The effect indicates efficient scattering of two pump polaritons, involving a biexciton intermediate state. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parametric scattering in semiconductor microcavities probed by four-wave mixing

We present a study of the polariton coherent dynamics in II–VI semiconductor microcavities in the parametric scattering regime. We perform angle resolved four-wave mixing, which allows us to study the polariton dephasing within the full reciprocal space. When polaritons are excited above the threshold in the phase matching conditions for parametric scattering, we observe a very efficient scattering towards the final states (signal and idler), inducing pump depletion. On the contrary, below threshold or when the phase matching conditions are not fulfilled, we observe an angle-dependent collision broadening that occurs when pump polaritons scatter towards the excitonic reservoir. We discuss the interplay between parametric scattering and collision broadening within the framework of a phenomenological numeric calculation. Last, we propose a new design for the realization of a vertical-cavity, surface emitting parametric oscillator/amplifier that provides triple resonance for the parametric frequencies together with cavity phase-matching for all waves at normal incidence.

Branch-entangled polariton pairs in planar microcavities and photonic wires

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 important role of nonlinear losses due to pair scattering into high-momentum exciton states is evaluated. The results show that the lack of protection of the pump polaritons in the upper branch is critical. In photonic wires, branch-entanglement of one-dimensional polaritons is achievable when the pump excites a lower polariton sub-branch at normal incidence, providing protection from the exciton reservoir.

Polariton parametric amplifier: pump dynamics in the coherent regime

We present a comprehensive study of the polariton coherent dynamics in II–VI semiconductor microcavities. An angle resolved four-wave mixing experiment has been developed, which allows us to study the polariton dephasing within the full reciprocal space. We observe two main trends: (i) pump polaritons that are excited above the threshold and in the phase matching condition for parametric amplification threshold are observed to scatter much more efficiently towards the final states (signal and idler), inducing pump depletion, and (ii) below this threshold or when the phase matching condition is not fulfilled, we observe an angle-dependent collision broadening, that occurs when pump polaritons can scatter towards the excitonic reservoir. Both dynamics are then analysed using a numerical model that reveals a complex interplay and competition between collision broadening and parametric amplification. In particular, it is shown how collision broadening must be taken into account in order to explain the gain saturation observed in the parametric amplification process. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Coherent picosecond vibron polaritons as probes of vibrational lifetimes

Picosecond pump-probe experiments on the C–O stretch vibration of acetic acid in solution with infrared pulses from a free-electron laser are presented. We show that under typical experimental conditions of pulses that are short compared to the inverse absorption linewidth and optically thick samples (necessary to observe significant transmission changes), the experimental pump-probe data are strongly influenced by pulse propagation effects (vibron polaritons) and coherent coupling between pump and probe vibron polaritons. To extract the vibrational lifetime from the data, it is therefore necessary to perform a full simulation of the propagation and coupling effects.