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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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Kordas, G., Witthaut, D., Buonsante, P. et al. The dissipative Bose-Hubbard model. Eur. Phys. J. Spec. Top. 224, 2127–2171 (2015). https://doi.org/10.1140/epjst/e2015-02528-2

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Keywords

  • European Physical Journal Special Topic
  • Master Equation
  • Phase Noise
  • Wigner Function
  • Dark Soliton