Solutions to the Jaynes-Cummings model without the rotating-wave approximation

TL;DR

This paper presents an exact solution to the Jaynes-Cummings model without the rotating-wave approximation using extended bosonic coherent states, applicable across all coupling strengths and detunings, especially relevant for ultra-strong coupling regimes.

Contribution

It introduces a method to solve the Jaynes-Cummings model exactly without the rotating-wave approximation using polynomial equations derived from extended bosonic coherent states.

Findings

Exact eigenvalues and eigenfunctions obtained for all coupling strengths.

Solution applicable to circuit QED systems in ultra-strong coupling.

Provides a comprehensive analytical framework for the model.

Abstract

By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation can give all eigenvalues and eigenfunctions of this model with all values of the coupling strength and the detuning exactly, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.