Phases of the electronic two-level model under the rotating wave approximation

TL;DR

This paper analyzes the time evolution and geometric phases of a two-level electronic system under the rotating wave approximation, highlighting the dependence on initial states and regimes like adiabatic and quasi-resonant.

Contribution

It provides a detailed calculation of the Aharonov-Anandan phase in the RWA, clarifying its dependence on initial conditions and regime-specific behaviors.

Findings

Aharonov-Anandan phase depends on initial state unless in adiabatic regime

In adiabatic regime, the phase reduces to Berry's phase

Results include behavior in quasi-resonant regime

Abstract

We present the time evolution of the electronic two-level model in the rotating wave approximation (RWA). We calculate the Aharonov-Anandan phase of the vector states with cyclic evolution either within the period of an external monochromatic electric field or the period corresponding to Rabi's frequency. The Aharonov-Anandan phase is shown to be dependent on the initial vector state, unless the system evolves in the adiabatic regime; in the latter case, the Aharonov-Anandan phase recovers Berry's phase. Our results are also discussed in the quasi-resonant regime.