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arXiv:1603.06897 · ACS Photonics

Dynamical Instability of a Nonequilibrium Exciton-Polariton Condensate

Nataliya Bobrovska, Michał Matuszewski, Konstantinos S. Daskalakis, Stefan Alexander Maier, Stéphane Kéna‐Cohen

Published Aug 10, 2017• 51 citations
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Abstract

By imaging single-shot realizations of an organic polariton quantum fluid, we observe the long-sought dynamical instability of nonequilibrium condensates. We find an excellent agreement between the experimental data and a numerical simulation of the open-dissipative Gross-Pitaevskii equation, without performing any parameter fitting, which allows us to draw several important conclusions about the physics of the system. We find that the reservoir dynamics are in the strongly nonadiabatic regime, which renders the complex Ginzburg–Landau description invalid. The observed transition from stable to unstable fluid can only be explained by taking into account the specific form of reservoir-mediated instability as well as particle currents induced by the finite extent of the pump spot.

DOI
10.1021/acsphotonics.7b00283

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Nature Communications•Jul 23, 2018•62 citations
By imaging single-shot realizations of an organic polariton quantum fluid, we observe the long-sought dynamical instability of nonequilibrium condensates. We find an excellent agreement between the experimental data and a numerical simulation of the open-dissipative Gross-Pitaevskii equation, without performing any parameter fitting, which allows us to draw several important conclusions about the physics of the system. We find that the reservoir dynamics are in the strongly nonadiabatic regime, which renders the complex Ginzburg–Landau description invalid. The observed transition from stable to unstable fluid can only be explained by taking into account the specific form of reservoir-mediated instability as well as particle currents induced by the finite extent of the pump spot.
Exciton–polariton condensates (EPCs) have emerged as a paradigmatic platform for investigating nonequilibrium quantum many-body phenomena, particularly due to their intrinsic open-dissipative nature and strong nonlinear interactions governed by the interplay between stimulated scattering and reservoir-mediated damping. Recent advances in Feshbach resonance engineering now enable precise tuning of interaction strengths, opening new avenues to explore exotic nonlinear excitations in these driven-dissipative systems. In this work, we systematically investigate the quench dynamics and stability of dark solitons in repulsive one-dimensional EPCs under sudden parameter variations in both nonlinear interaction strength g and pump intensity P. Through a Hamiltonian variational approach that incorporates reservoir damping effects, we derive reduced equations of motion for soliton velocity evolution that exhibit remarkable qualitative agreement with direct numerical simulations of the underlying open-dissipative Gross–Pitaevskii equation. Our results reveal three distinct dynamical regimes: (i) stable soliton propagation at intermediate pump powers, (ii) velocity-dependent soliton breakup above critical pumping thresholds, and (iii) parametric excitation of soliton trains under simultaneous interaction quenches. These findings establish a quantitative framework for understanding soliton dynamics in nonresonantly pumped EPCs, with implications for quantum fluid dynamics and nonequilibrium Bose–Einstein condensates.
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We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation and small density fluctuations approximation that allow one to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of these approximations can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation.
Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations and instabilities, which can strongly influence the condensate formation. Using optical trapping and homodyne detection, we directly access the photon statistics and second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0) of the condensate. We show that polariton condensation near the threshold is not a purely static transition, but instead undergoes a dynamical regime characterized by stochastic hopping between condensed and non-condensed states. These intermittent dynamics are accompanied by a gradual reduction of g(2)(0)g^{(2)}(0)g(2)(0) towards unity, revealing the progressive build-up of coherence even in the presence of strong temporal fluctuations. Numerical simulations, based on a stochastic Truncated Wigner description of the driven-dissipative polariton field, reproduce these dynamics and capture the essential role of noise and reservoir interactions. This work demonstrates that the observed temporal hopping is an intrinsic feature of polariton condensation, providing a dynamical perspective that goes beyond static descriptions of the condensation phase transition.
Dynamics of exciton-polariton condensates under continuous-wave incoherent Gaussian optical pumping is considered. It is shown that the conventional supercritical Stuart-Landau picture is invalid in a certain domain of the parameter space. For strong polariton repulsion from the reservoir and relatively small pump spots, the dynamics is adequately described by the quintic Stuart-Landau equation. The corresponding subcritical pitchfork bifurcation leads to condensate formation, accompanied by bistability between the trivial and nontrivial states over a finite pump-power range and a one-bit memory. Further increase of the repulsion parameter or decrease of the spot size breaks down the perturbative approach and leads to a peculiar self-trapping regime with complex dynamics. Experimental evidence of the emergence of the proposed behavior is provided. Our findings can be used to design polaritonic setups that exploit the predicted memory effect.
A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.