On the rotating wave approximation in the adiabatic limit

TL;DR

This paper investigates the validity of the rotating wave approximation in quantum optics, revealing it generally fails in the adiabatic limit due to topological differences between models, affecting Berry phase calculations.

Contribution

It demonstrates that the rotating wave approximation breaks down in the adiabatic limit, highlighting topological reasons and differences in Berry phases between the Jaynes-Cummings and Rabi models.

Findings

The Rabi model's Berry phase is zero, unlike the Jaynes-Cummings model.

The approximation fails in the adiabatic limit regardless of parameters.

Topological differences explain the breakdown of the approximation.

Abstract

I revisit a longstanding question in quantum optics; When is the rotating wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes-Cummings model. The source of this surprising result is traced back to different topologies in the two models.