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 non-collective dissipators. Exploiting the permutation symmetry in our model, we employ a phase space approach for the solution of this equa...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: Merkel, Konrad, Link, Valentin, Luoma, Kimmo, Strunz, Walter T
Format: Article
Language:English
Subjects:
Entanglement
Fokker-Planck equation
Mean field theory
Permutations
Theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2006.03264