Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

TL;DR

This paper derives analytical solutions for the anisotropic Rabi model, revealing how counter-rotating terms influence quantum properties and the validity of the rotating-wave approximation across different coupling regimes.

Contribution

It provides approximate analytical energy spectra and wavefunctions for the anisotropic Rabi model, including effects of counter-rotating terms, validated by numerical results.

Findings

Analytical spectra agree with numerical calculations across parameter ranges.

Counter-rotating terms act as parameter shifts in the weak coupling limit.

Breakdown of U(1)-symmetry and deviations from the Jaynes-Cummings model are demonstrated.

Abstract

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.