Dynamical and Steady State Properties of a Bose-Hubbard Chain with Bond-Dissipation: A Study based on Matrix Product Operators

TL;DR

This paper investigates the steady state and dynamical properties of a dissipative Bose-Hubbard chain using matrix product operators, revealing complex steady states and relaxation dynamics influenced by engineered dissipation and interactions.

Contribution

It introduces a superoperator approach with matrix product operators to analyze the steady state and transient dynamics of a dissipative Bose-Hubbard chain, highlighting the interplay between Hamiltonian and dissipative effects.

Findings

Steady state stabilizes a BEC condensate wave function.

Identification of a non-trivial steady state due to competing dynamics.

Observation of dissipative gap closing in the thermodynamic limit.

Abstract

We study a dissipative Bose-Hubbard chain subject to an engineered bath using a superoperator approach based on matrix product operators. The dissipation is engineered to stabilize a BEC condensate wave function in its steady state. We then characterize the steady state emerging from the interplay between incompatible Hamiltonian and dissipative dynamics. While it is expected that interactions lead to this competition, even the kinetic energy in an open boundary condition setup competes with the dissipation, leading to a non-trivial steady state. We also present results for the transient dynamics and probe the relaxation time revealing the closing of the dissipative gap in the thermodynamic limit.