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Journal of Experimental and Theoretical Physics

Hard mode of stimulated scattering in the system of quasi-two-dimensional exciton polaritons

Sergei S. Gavrilov, Николай Алексеевич Гиппиус, V. D. Kulakovskiĭ, S. G. Tikhodeev

Published May 1, 2007• 20 citations
Publisher

Abstract

Dynamics of stimulated scattering of quasi-two-dimensional exciton polaritons in a semiconductor microcavity is considered theoretically. A system possessing a bistable response to coherent excitation is studied. Being a system of weakly interacting Bose particles under strongly nonequilibrium conditions, it exhibits a complex dynamics of the development of condensate modes. It is shown that multimode instability can arise in a threshold way in the system under a smooth increase in pump intensity. In this case, rapid populating of a multitude of unstable modes leads to stochastization of scattering, and evolution to a quasi-steady macrostate is performed as self-organization in an open nonequilibrium system. Arising fluctuations lead to the occurrence of a spatial nonuniformity of the distribution of scattered states.

DOI
10.1134/s1063776107050056

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Dynamics of stimulated scattering of quasi-two-dimensional exciton polaritons in a semiconductor microcavity is considered theoretically. A system possessing a bistable response to coherent excitation is studied. Being a system of weakly interacting Bose particles under strongly nonequilibrium conditions, it exhibits a complex dynamics of the development of condensate modes. It is shown that multimode instability can arise in a threshold way in the system under a smooth increase in pump intensity. In this case, rapid populating of a multitude of unstable modes leads to stochastization of scattering, and evolution to a quasi-steady macrostate is performed as self-organization in an open nonequilibrium system. Arising fluctuations lead to the occurrence of a spatial nonuniformity of the distribution of scattered states.
A transient spectroscopy technique for studying near-condensate modes of exciton polaritons in high-quality-factor planar semiconductor microcavities is proposed. It is demonstrated that, under the conditions of coherent external pumping, the transition to the upper steady state of an optically bistable condensate is accompanied by the excitation of near-condensate modes. They manifest themselves in the appearance of transient oscillations of the polariton intensity as the system switches to the upper branch of the S-shaped bistable pump dependence of the intensity. Analysis of the time-resolved spectra of these oscillations provides information on interactions in the system and the evolution of the exciton-polariton condensate density.
A physical mechanism of the implementation of undamped Rabi oscillations in the system of exciton polaritons in a semiconductor microcavity in the presence of nonresonant pumping has been proposed. Various mechanisms of the stimulated scattering of excitons from the reservoir have been considered. It has been shown that undamped oscillations of the population of the photon component of the condensate can be caused by the feeding of a coherent Rabi oscillator owing to the pair scattering of excitons from the reservoir to the ground state. The effect should be observed in spite of a more intense relaxation of polaritons of the upper branch observed experimentally.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
We develop a theory for the dynamics of the density matrix describing a multimode polariton condensate. In such a condensate several single-particle orbitals become highly occupied, due to stimulated scattering from reservoirs of high-energy excitons. A generic few-parameter model for the system leads to a Lindblad equation which includes saturable pumping, decay, and condensate interactions. We show how this theory can be used to obtain the population distributions, and the time-dependent first- and second-order coherence functions, in such a multimode condensate. As a specific application, we consider a polaritonic Josephson junction, formed from a double-well potential. We obtain the population distributions, emission line shapes, and widths (first-order coherence functions), and predict the dephasing time of the Josephson oscillations.
We investigate the physics of coherent polaritons in a double-well configuration under a resonant pumping. For a continuous-wave pump, bistability and self-pulsing regimes are identified as a function of the pump energy and intensity. The response to an additional probe pulse is characterized in the different cases and related to the Bogoliubov modes around the stationary state. Under a pulsed pump, a crossover from Josephson-like oscillations to self-trapping is predicted for increasing pump intensity. The accurateness of the effective two-mode model is assessed by comparing its predictions to a full solution of the nonequilibrium Gross--Pitaevskii equation.