Exact solvability of the quantum Rabi models within Bogoliubov operators

TL;DR

This paper presents a simplified and physically intuitive method for the exact solution of quantum Rabi models using Bogoliubov operators, extending to multi-level and multi-mode systems.

Contribution

It introduces an alternative approach employing Bogoliubov operators for exact solutions of quantum Rabi models, avoiding complex conditions used in previous methods.

Findings

Exact solutions for one-photon and two-photon Rabi models obtained

Extended coherent and squeeze states form the basis of solutions

Method applicable to multi-level and multi-mode spin-boson systems

Abstract

The quantum Rabi model can be solved exactly by the Bargmann transformation from real coordinate to complex variable recently [Phys. Rev. Lett. \textbf{107}, 100401 (2011)]. By the extended coherent states, we recover this solution in an alternative simpler and perhaps more physical way without uses of any extra conditions, like Bargmann conditions. In the same framework, the two-photon Rabi model are solved exactly by extended squeeze states. Transcendental functions have been derived with the similar form as those in one-photon model. Both extended coherent states and squeeze states are essentially Fock states in the space of the corresponding Bogoliubov operators. The present approach could be easily extended to study the exact solvability or integrability of various spin-boson systems with multi-level, even multi-mode.