Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED

TL;DR

This paper demonstrates that Berry phases in cavity QED systems only appear when the rotating wave approximation is used, showing that without it, such phases do not occur, challenging previous claims.

Contribution

The study reveals that the presence of Berry phases in cavity QED depends on the RWA, providing a geometrical interpretation and highlighting potential false conclusions from RWA-based analyses.

Findings

Berry phases vanish without the RWA in cavity QED

Conical intersections are absent without the RWA

RWA can lead to false conclusions in the Jaynes-Cummings model

Abstract

We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the {\it rotating wave approximation} (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semi-classical energy surfaces which in a simple way brings out the phase space dynamics. With the RWA, a conical intersection between the surfaces emerges and encircling it gives rise to the Berry phase. Without the RWA, the conical intersection is absent and therefore the Berry phase vanishes. It is believed that this is a first example showing how the application of the RWA in the Jaynes-Cummings model may lead to false conclusions, regardless mutual strengths between the system parameters.