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

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 nonunitary 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 nonunitary evolution. This fact is supported with a geometrical explanation as well.