Phase space theory for open quantum systems with local and collective dissipative processes

In this article we investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and local dissipators. Exploiting the permutation symmetry in our model, we employ a phase space approach for the solution of this equation in terms of a diagonal representation with respect to certain generalized spin coherent states. Remarkably, this allows to interpolate between mean field theory and finite system size in a formalism independent of Hilbert-space dimension. Moreover, in certain parameter regimes, the evolution equation for the corresponding quasiprobability distribution resembles a Fokker-Planck equation, which can be efficiently solved by stochastic calculus. Then, the dynamics can be seen as classical in the sense that no entanglement between the two-level systems is generated. Our results expose, utilize and promote techniques pioneered in the context of laser theory, which can be powerful tools to investigate problems of current theoretical and experimental interest.

Automated summary

This article investigates the driven dissipative quantum dynamics of an ensemble of two-level systems, showing the possibility of interpolating between mean field theory and finite system size by exploiting permutation symmetry and a phase space approach. It also reveals that in certain parameter regimes, the evolution equation for the corresponding quasiprobability distribution resembles a Fokker-Planck equation, which can be efficiently solved by stochastic calculus. The results demonstrate classical-like dynamics with no entanglement generation between the two-level systems, utilizing and promoting techniques pioneered in the context of laser theory as powerful tools for investigating current theoretical and experimental problems.