On analytic solutions of the driven, 2-photon and two-mode quantum Rabi models

TL;DR

This paper derives analytic solutions for the driven, 2-photon, and two-mode quantum Rabi models using Bogoliubov transformations and Bargmann-Hilbert spaces, providing a method to determine their energy spectra.

Contribution

It introduces a unified analytic approach to solve complex quantum Rabi models without ${\

Findings

Analytic transcendental functions for the models' solutions.

Zeros of these functions determine the energy spectra.

Method enables numerical computation of spectra using root-search techniques.

Abstract

By applying the Bogoliubov transformations and through the introduction of the Bargmann-Hilbert spaces, we obtain analytic representations of solutions to the driven Rabi model without ${\cal Z}_2$ symmetry, and the 2-photon and two-mode quantum Rabi models. In each case, transcendental function is analytically derived whose zeros give the energy spectrum of the model. The zeros can be numerically found by standard root-search techniques.