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

TL;DR

This paper develops a phase space approach to analyze driven dissipative quantum dynamics of two-level systems, bridging mean-field and finite-size regimes, and revealing classical-like evolution without entanglement.

Contribution

It introduces a novel phase space method leveraging permutation symmetry to solve Markovian master equations for collective and local dissipation in quantum ensembles.

Findings

Allows interpolation between mean-field and finite-size regimes

Resembles a Fokker-Planck equation in certain regimes

Demonstrates classical-like dynamics without entanglement

Abstract

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 non-collective 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 we now apply to problems of current theoretical and experimental interest.