Variational analysis of driven-dissipative bosonic fields

Abstract

We present a method to perform a variational analysis of the quantum master equation for drivendisspative bosonic fields with arbitrary large occupation numbers. Our approach combines the P representation of the density matrix and the variational principle for open quantum system. We benchmark the method by comparing it to wave-function Monte-Carlo simulations and the solution of the Maxwell-Bloch equation for the Jaynes-Cummings model. Furthermore, we study a model describing Rydberg polaritons in a cavity field and introduce an additional set of variational paramaters to describe correlations between different modes.

Unpredictability and entanglement in open quantum systems

“…The strategy behind VQS is to consider a variational parametrization of the state ρ(t + τ ) after a continuous timestep τ , given the state ρ(t) at time t and the dynamics according to the quantum master equation. Our approach is based on the variational principle for open quantum systems [50], which also has been generalized towards variational approximation of the time evolution, both in the Schrödinger [51] and in the Heisenberg picture [52]. Within the latter, one can introduce a variational cost functional F v given by…”

“…which realizes a discretized version of the master equation that is correct up to second order in τ . Crucially, the sum does not need to run over a complete set of observables to achieve accurate results [52].…”