Solutions to the anisotropic quantum Rabi model

TL;DR

This paper develops analytical solutions for the anisotropic quantum Rabi model using extended coherent states, providing a unified approach that includes adiabatic and generalized rotating-wave approximations, applicable across various coupling strengths.

Contribution

It introduces a novel analytical framework using two types of extended coherent states to solve the anisotropic quantum Rabi model, unifying different approximation methods.

Findings

Derived a G-function for regular and exceptional solutions.

Established a general scheme for eigensolutions analytically.

Generalized rotating-wave approximations are effective over wide parameter ranges.

Abstract

In this work, the anisotropic quantum Rabi model with different coupling strengths of the rotating-wave and counter-rotating wave terms is studied by using two kinds of extended coherent states (ECS). By the first kind of ECS, we can derive a so-called $G$-function, by which both the regular and exceptional solutions can be given. The exceptional solution are just corresponding to the crossing points of two energy levels with different parities, so is doubly degenerate. By the second kind of ECS, a general scheme for the eigensolutions is derived analytically in a unified way. The zero-order approximation is just the adiabatic approximation, and the first-order approximation is actually a generalized rotating-wave approximation. The algebraic formulae for the eigensolutions are given explicitly in two approximations. The generalized rotating-wave approximations work well in a wide range of two different coupling strengths and the qubit detunings.