Parameter-dependent unitary transformation approach for quantum Rabi model

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.