The dissipative Bose-Hubbard model

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 counterintuitive 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.

Non‐equilibrium dynamics in dissipative Bose‐Hubbard chains

“…In the presence of dissipation the dynamics is usually given by a master equation in Lindblad form [4,11,[13][14][15][16][17][18][19][20][21] …”

Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains

“…This choice of the Lindblad operator, as shown in [7], leads to equations of motion for the SPDM equivalent to the heuristic non-Hermitian discrete nonlinear Schrödinger equation introduced in [23] and successfully applied to the description of localized single-body dissipation processes in Bose-Hubbard chains in good agreement with experimental realizations [3,5]. Further sets of Lindblad operators modelling other processes in Bose-Hubbard chains can be found in the review [24].…”

“…This suppression is a signature of the so-called quantum Zeno effect, meaning that particles are blocked on average from flowing into the site with dissipation, see e.g., the results and descriptions in [3,24,27]. Dissipation can thus induce an effectively self-trapped regime, considerably lowering the average inter-well tunnelling, although the values of the population imbalance and the interaction strength do not suffice to reach this regime in the absence of dissipation.…”

Microscopic models of source and sink for atomtronics

“…which is usually used to model the particle reservoirs [26][27][28][29]. In fact, providing the conditions of QC are satisfied, we can derive Eq.…”