Jaynes-Cummings model without rotating wave approximation. Asymptotics of eigenvalues

TL;DR

This paper develops a perturbation theory for the Jaynes-Cummings model without the rotating wave approximation, providing asymptotic eigenvalue formulas that account for counter-rotating terms at high quantum numbers.

Contribution

It introduces a novel perturbation approach using transition frequency as a parameter and derives exact eigenvalue asymptotics including counter-rotating effects.

Findings

Counter-rotating terms alter the second term of the eigenvalue asymptotics.

The perturbation series converges with estimable remainder terms.

High quantum number eigenvalues are characterized by explicit asymptotic formulas.

Abstract

In this paper the perturbation theory with the frequency of transition in atom as perturbation parameter is constructed. The estimation of the reminder term of series of this perturbation theory is given. With the help of this perturbation theory we have found an exact asymptotics of eigenvalues of complete hamiltonian in the limit of high quantum numbers. It is shown that the counter-rotating terms keep a leading term but absolutely change a second term of this asymptotic.