Concise analytic solutions to the quantum Rabi model with two arbitrary qubits

TL;DR

This paper presents a concise, exact analytical solution to the two-qubit quantum Rabi model using extended coherent states, deriving G-functions and identifying eigenvalues, including exceptional ones, with practical applications.

Contribution

It introduces a simplified, exact analytical approach for the two-qubit quantum Rabi model, deriving G-functions and eigenvalues in a clear, practical manner.

Findings

Derived G-functions with 2x2 determinants for the two-qubit QRM.

Obtained the entire regular spectrum from zeros of the G-function.

Identified exceptional eigenvalues and dark states explicitly.

Abstract

Using extended coherent states, an analytical exact study has been carried out for the quantum Rabi model (QRM) with two arbitrary qubits in a very concise way. The $G$-functions with $2 \times 2$ determinants are generally derived. For the same coupling constants, the simplest $G$-function, resembling that in the one-qubit QRM, can be obtained. Zeros of the $G$-function yield the whole regular spectrum. The exceptional eigenvalues, which do not belong to the zeros of the $G$ function, are obtained in the closed form. The Dark states in the case of the same coupling can be detected clearly in a continued-fraction technique. The present concise solution is conceptually clear and practically feasible to the general two-qubit QRM and therefore has many applications.