Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: a c-field model

Abstract

Developing theoretical models for nonequilibrium quantum systems poses significant challenges. Here we develop and study a multimode model of a driven-dissipative Josephson junction chain of atomic Bose-Einstein condensates, as realised in the experiment of Labouvie et al.[Phys. Rev. Lett. 116, 235302 (2016)]. The model is based on c-field theory, a beyond-mean-field approach to Bose-Einstein condensates that incorporates fluctuations due to finite temperature and dissipation. We find the c-field model is capable of capturing all key features of the nonequilibrium phase diagram, including bistability and a critical slowing down in the lower branch of the bistable region. Our model is closely related to the so-called Lugiato-Lefever equation, and thus establishes new connections between nonequilibrium dynamics of ultracold atoms with nonlinear optics, exciton-polariton superfluids, and driven damped sine-Gordon systems.

Variational truncated Wigner approximation for weakly interacting Bose fields: Dynamics of coupled condensates

“…In order to accurately describe the non-equilibrium dynamics of Bose condensates of atoms it is often necessary to treat the weakly interacting gas beyond the mean-field level [1], in particular if modes with low occupation become relevant. Prime examples, where such modes play an important role, are driven dissipative Bose gases with multi-stable stationary states or the filling dynamics of coupled condensates [2][3][4][5][6][7][8][9]. An approach, widely used in quantum optics, that takes both thermal and leading-order quantum fluctuations into account, is the truncated Wigner approximation (TWA) [10][11][12][13][14][15][16][17][18].…”