The Dissipative Bose-Hubbard Model. Methods and Examples

TL;DR

This paper reviews theoretical and numerical methods for modeling open ultracold bosonic systems with dissipation, highlighting diverse approaches and results in one-dimensional lattice setups.

Contribution

It introduces a coherent-state path integral formalism for dissipative many-body bosonic systems, complementing existing numerical techniques.

Findings

Demonstrates various numerical methods for dissipative bosonic systems

Presents results on ultracold bosons in 1D lattices

Introduces a Feynman-Vernon based path integral approach

Abstract

Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.