Simulating Many-Body Open Quantum Systems Beyond the Born-Markov Approximation

Ultra-cold atomic systems offer a controllable way of probing the effects of dissipative processes on the dynamics of many-body systems in regimes that go beyond those typical in quantum optics, such as out with a Born-Markov approximation. It is also desirable to develop numerical tools for theoretically analysing these systems, however this requires additions to conventional quantum trajectory techniques as these are only valid when a Lindblad master equation could be used to describe the dynamics. 

Here we combine the recently developed algorithm the hierarchy of pure states (HOPS) [1] and tensor network methods which now allow us to simulate open many-body systems (in 1D) that are strongly coupled to a non-Markovian reservoir. As a first example, we benchmark this method by applying it to a Hubbard-Holstein model with dissipative phonon modes, where we demonstrate that this approach can capture features beyond what is capable with standard open quantum system techniques. We also discuss future generalisations of this method which for example may allow for the simulation of current experiments exploring the dynamics of impurity atoms immersed in Bose-Einstein condensates. 

 

[1] - D. Suess, et. al, PRL 113, 150403 (2014)