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

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Abstract

In this paper, a non-Markovian version of the Gross–Pitaevskii equation is proposed to describe the condensate formation in an exciton–polariton system subject to incoherent pumping. By introducing spatially delta-correlated noise terms, we observe a transition from a spatially ordered phase to a disordered one with simultaneous density reduction as the temperature increases. Above the transition temperature, the uniform condensate breaks up into multiple irregularly located separate dense spots. Using the Gabor transform, we demonstrate condensate decoherence with increasing temperature, which is accompanied by the transition from narrow-band to broadband spectral density.

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Acknowledgements

The authors are grateful to anonymous referees for valuable comments and to M. Uleysky for the assistance in the preparation of figures. The work of A. Alliluev and D. Makarov is supported by the Laboratory of Nonlinear Hydrophysics and Natural Hazards of the V.I.Il’ichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, within the project of the Ministry of Science and Higher Education of the Russian Federation, agreement number 075-15-2022-1127. N. Asriyan is supported by the foundation for the advancement of theoretical physics and mathematics “Basis”. Yu. Lozovik’s work is supported by the Russian Science Foundation (RSF) in the scope of the project 23-12-00115.

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Authors and Affiliations

  1. V. I. Il’ichev Pacific Oceanological Institute, Far East Branch of the Russian Academy of Sciences, Vladivistok, Russia, 690041

    Alexey D. Alliluev & Denis V. Makarov

  2. N.L. Dukhov Research Institute of Automatics (VNIIA), Moscow, Russia, 127030

    Norayr A. Asriyan & Andrei A. Elistratov

  3. Institute for Spectroscopy RAS, Troitsk, Russia, 108840

    Yurii E. Lozovik

  4. MIEM, National Research University Higher School of Economics, Moscow, Russia, 101000

    Yurii E. Lozovik

  5. Institute of Microelectronics Technology RAS, Chernogolovka, Russia, 142432

    Norayr A. Asriyan

Authors
  1. Alexey D. Alliluev
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  2. Denis V. Makarov
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  3. Norayr A. Asriyan
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  4. Andrei A. Elistratov
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  5. Yurii E. Lozovik
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Contributions

YE supervised this work. DV, NA and AA contributed to the theoretical part of the paper. AD and DV performed the numerical simulations. DV and NA contributed to writiing of the text. AD prepared illustrations for the paper.

Corresponding author

Correspondence to Denis V. Makarov.

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Alliluev, A.D., Makarov, D.V., Asriyan, N.A. et al. Non-Markovian Stochastic Gross–Pitaevskii Equation for the Exciton–Polariton Bose–Einstein Condensate. J Low Temp Phys 214, 331–343 (2024). https://doi.org/10.1007/s10909-023-03027-4

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  • DOI: https://doi.org/10.1007/s10909-023-03027-4

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