Non-equilibrium steady states and critical slowing down in the dissipative Bose-Hubbard model

TL;DR

This paper investigates the non-equilibrium steady states and critical slowing down in the dissipative Bose-Hubbard model, using classical field and Wigner methods to analyze large chains with localized losses.

Contribution

The authors develop a compact effective model for large dissipative Bose-Hubbard chains that accurately captures stationary states and hysteresis, and analyze fluctuations and switching dynamics.

Findings

Mean-field approach reproduces stationary states well

Dark soliton states are preserved in the model

Effective Liouvillian gap underestimates fluctuations

Abstract

Motivated by recent experiments, we study the properties of large Bose-Hubbard chains with single-particle losses at one site using classical field methods. We construct and validate a compact effective model that reduces computations to only a few sites. We show that in the mean-field approach the description captures the stationary states of the dissipative mode very well. Not only is there a good quantitative agreement in the hysteresis loop, the dark soliton state can be reproduced as well due to the the preservation of the $U(1)$ symmetry. Bimodality of the steady states, observed on longer timescales, is studied using the truncated Wigner method. We compare the switching statistics and derive the effective Liouvillian gap in function of the tunneling, showing that the effective description underestimates fluctuations.