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arXiv:2311.13561 · Physical Review A

Driven-dissipative Bose-Einstein condensation and the upper critical dimension

Yikang Zhang, Thomas Barthel

Published Feb 23, 2024• 2 citations
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Abstract

In open quantum systems, Bose-Einstein condensates can be stabilized by driving and dissipation. The authors analyze the phenomenon with Keldysh field theory and, below the upper critical dimension, with a renormalization-group analysis.
DOI
10.1103/physreva.109.l021301

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We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite lifetime of the condensed particles, and energy relaxation. The coupling between the reservoir and the condensate is described with semiclassical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyze the main properties of a condensate described by this hybrid Boltzmann--Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first-order coherence, dynamic and energetic stability, and drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfills the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs as it moves at a velocity smaller than the speed of excitations. First-order spatial coherence of the condensate is found to decay exponentially in one dimension and with a power law in two dimensions, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite lifetime of the condensate excitations. We compare these properties with those of a condensate described by the popular ``diffusive'' models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.
Driven-dissipative quantum many-body systems, i.e., many-particle systems where quantum coherent dynamics and dissipative effects occur on the same footing, can constitute a promising platform to initiate a systematic classification of quantum dynamical criticality. In this work, the authors show that both nonequilibrium and quantum features can be simultaneously present and persist in the low-frequency properties of a critical one-dimensional driven open Bose gas, and no effective equilibrium description is applicable for this novel type of nonequilibrium quantum criticality.