The Dissipative Bose-Hubbard Model. Methods and Examples

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.

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Cited by in corpus (46)

• One-dimensional many-body entangled open quantum systems with tensor network methods
• Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array
• Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss
• One-dimensional spin-1/2 fermionic gases with two-body losses: weak dissipation and spin conservation
• Landauer-Büttiker equation for bosonic carriers
• NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition
• Out-of-equilibrium steady states of a locally driven lossy qubit array
• The open Bose-Hubbard chain: Pseudoclassical approach
• Doublons, topology and interactions in a one-dimensional lattice
• Spectral analysis of two-dimensional Bose-Hubbard models
• Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
• Quantum droplets with particle imbalance in one-dimensional optical lattices
• Stable bipolarons in open quantum systems
• Negative differential conductivity and quantum statistical effects in a three-site Bose-Hubbard model
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