Abstract
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 [1].
Highlights
The coupling of quantum matter to quantum light has been achieved in numerous experimental platforms
We described in detail two methods capable of tackling both short and global range interactions of an interacting many-body system coupled to a single dissipative bosonic mode
We benchmark the methods with the example of a Bose-Hubbard chain coupled to an optical cavity
Summary
The coupling of quantum matter to quantum light has been achieved in numerous experimental platforms. This method is numerically exact and can deal with small to intermediate system sizes Whereas these methods are very generally applicable for quantum many-body systems with short-range interaction coupled globally to a single dissipative bosonic mode, we benchmark the presented methods for a Bose-Hubbard chain coupled to a cavity mode and transversely pumped with a standing-wave laser beam. The particles can for example describe atoms or electrons and the bosonic quantum field can be for example a photonic field of a cavity or a long-lived phononic mode These systems can be described by a Lindblad equation for the density operator ρ given by [8,17,35,36].
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