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arXiv:2212.07152 · Journal of Low Temperature Physics

Non-Markovian Stochastic Gross–Pitaevskii Equation for the Exciton–Polariton Bose–Einstein Condensate

Alexey Dmitrievich Alliluev, Денис В. Макаров, Norayr Armenovich Asriyan, Andrei A. Elistratov, Yu. E. Lozovik

Published Jan 9, 2024• 8 citations
arXivHTMLPDF
DOI
10.1007/s10909-023-03027-4

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Dynamics of exciton-polaritonic condensate under incoherent pumping is studied using the non-Markovian stochastic Gross-Pitaevskii equation with the pseudo-differential dispersion term. This term corresponds to the lower energy branch of polaritons. It is shown that an increasing of the pumping spot area leads to the appearance of various spatial structures whose properties depend on the duration of the dynamical memory. In the regime of short memory time, condensate can form an extended state that spans outside the pumping area. We conclude that onset of such extended states is related to the specific form of the dispersion term causing the ``traffic jam'' effect. The case of long memory time corresponds to enhanced condensate formation, when increasing of the pumping area leads to appearance of angular condensate structures which partially suppress emission of matter waves from the pumping area.
Abstract The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir.
Dynamics of exciton-polariton Bose‒Einstein condensate in an optical microcavity is considered. A novel version of stochastic Gross‒Pitaevsky equation for description of condensate evolution under non-Markovian interaction with environment is proposed. Using the proposed version, analysis of condensate dynamics for various temperatures is carried out. The phase transition from a homogeneous to fragmented condensate state near temperature of 15 K is found. This phase transition is accompanied by drop of condensate density and decrease of correlation length. It is found that correlation length oscillates with time for the temperature of 10 K. The results obtained indicate the necessity to take into account non-Markovianity of condensate interaction with the excitonic reservoir.