Jaynes-Cummings model: What emerges first beyond the rotating-wave approximation?

TL;DR

This paper provides an exact solution to the Jaynes-Cummings model beyond the rotating-wave approximation, revealing the effects of counter-rotating terms and applicable to ultra-strong coupling regimes.

Contribution

It introduces an extended analytical approach to solve the Jaynes-Cummings model without RWA, capturing counter-rotating effects explicitly.

Findings

Analytical expressions valid in ultra-strong coupling regime

Counter-rotating terms significantly affect system dynamics

Successful application to vacuum Rabi splitting

Abstract

The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by extended Swain's ansatz with the conserved parity. The analytical approximations are then performed at different levels. The well-known rotating-wave approximation is naturally covered in the present zero and first approximations. The effect of the counter rotating-wave term emerges clearly in the second order approximation. The concise analytical expressions are given explicitly and can be applicable up to the ultra-strong coupling regime. The preliminary application to the vacuum Rabi splitting is shown to be very successful.