Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness

TL;DR

This paper investigates the geometric phases in both ideal and dissipative Jaynes-Cummings models, revealing that resonance conditions lead to robust geometric phases unaffected by environmental dissipation.

Contribution

It introduces a generalized kinematic approach to compare geometric phases in unitary and dissipative models, providing new insights into environmental effects on quantum phase robustness.

Findings

Geometric phases are robust at resonance despite dissipation.

The approach allows detailed comparison of environmental effects.

Geometric interpretation explains phase behavior under dissipation.

Abstract

We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of the (cavity) electromagnetic field, in a perfect or dissipative cavity respectively. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls and the incoherent pumping of the two-level system. Our approach allows to compare the geometric phases acquired in these models, leading to an exhaustive characterization of the corrections introduced by the presence of the environment. We also provide geometric interpretations for the observed behaviors. When the resonance condition is satisfied, we show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution. This fact is supported with a geometrical explanation as well.