Parametric approximation as open quantum systems problem

TL;DR

This paper presents a systematic open quantum systems approach to the parametric approximation, deriving non-unitary corrections and analyzing non-Markovian effects in the dissipative Jaynes-Cummings model.

Contribution

It introduces a perturbative correction framework for the parametric approximation within open quantum systems, including non-Markovian dynamics and Lamb-shift effects.

Findings

Non-unitary corrections to the parametric approximation are derived.

Non-Markovian effects are significant before depletion at high detuning.

Initial non-Markovian behavior influences post-depletion dynamics.

Abstract

In this work we develop an open quantum system view of the parametric approximation, which allows us to obtain systematic perturbative corrections to it. We consider the Jaynes-Cummings model with dissipation, assuming that the field is in the regime close to the parametric approximation with depletion. We obtain non-unitary corrections to the parametric approximation and additional dynamical Lamb-shift contributions to it. For high detuning, these non-unitary corrections appear to be non-Markovian before depletion. And we show that even after depletion, initial non-Markovian behaviour contributes to the dynamics via laser-induced polishing of the density matrix.