Parameter-dependent unitary transformation approach for quantum Rabi model

TL;DR

This paper presents an exact analytical solution to the quantum Rabi model using a parameter-dependent unitary transformation, providing explicit energy spectra and eigenfunctions across all parameters, revealing potential physical phenomena due to degeneracies.

Contribution

The paper introduces a novel exact solution method for the quantum Rabi model employing parameter-dependent unitary transformations, applicable in both occupation number and Bargmann space.

Findings

Complete energy spectrum derived analytically

Eigenfunctions expressed as convergent series

Identification of degeneracies leading to physical phenomena

Abstract

Quantum Rabi model has been exactly solved by employing the parameter-dependent unitary transformation method in both the occupation number representation and the Bargmann space. The analytical expressions for the complete energy spectrum consisting of two double-fold degenerate sub-energy spectra are presented in the whole range of all the physical parameters. Each energy level is determined by a parameter in the unitary transformation, which obeys a highly nonlinear equation. The corresponding eigenfunction is a convergent infinite series in terms of the physical parameters. Due to the level crossings between the neighboring eigenstates at certain physical parameter values, such the degeneracies could lead to novel physical phenomena in the two-level system with the light-matter interaction.