We present two approaches capable of describing the dynamics of an interacting many-body system on a lattice coupled globally to a dissipative bosonic mode. Physical realizations are, for example, ultracold atom gases in optical lattice coupled to a photonic mode of an optical cavity or electronic gases in solids coupled to THz cavity fields. The first approach, applicable for large dissipation strengths and any system size, is a variant of the many-body adiabatic elimination method for investigating the long-time dynamics of the system. The second method extends the time-dependent matrix product techniques to capture the global coupling of the interacting particles to the bosonic mode and its open nature. It gives numerically exact results for small to intermediate system sizes. As a benchmark for our methods we perform the full quantum evolution of a Bose-Hubbard chain coupled to a cavity mode. We show that important deviations from the mean-field behavior occur when considering the full atoms cavity coupling [C.-M. Halati, A. Sheikhan, H. Ritsch, and C. Kollath, Phys. Rev. Lett. 125, 093604 (2020)].

中文翻译：

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治疗整体耦合到相互作用的多体系统的单一耗散玻色子模式的理论方法

我们提出了两种方法，它们能够描述相互作用的多体系统在全局耦合到耗散的玻色子模式的晶格上的动力学。物理实现是，例如，与光腔的光子模式耦合的光学晶格中的超冷原子气体，或与THz腔场耦合的固体中的电子气体。第一种方法适用于较大的耗散强度和任何系统尺寸，是用于研究系统长期动力学的多体绝热消除方法的一种变体。第二种方法扩展了与时间有关的矩阵乘积技术，以捕获相互作用粒子与玻色子模式及其开放性质的全局耦合。对于中小型系统，它给出了数值精确的结果。作为我们方法的基准，我们执行了耦合到腔模的Bose-Hubbard链的完整量子演化。我们表明，当考虑全原子腔耦合[C.M]时，会发生与平均场行为的重要偏离。Halati，A。Sheikhan，H.Ritsch和C.Kollat​​h，物理 牧师 125，093604（2020）]。