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

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 ${\mathcal{Z}}_2$ 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.

LaTex 16 pages. Updated version

References in corpus (6)

• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Integrability vs Quantum Thermalization
• On solvability and integrability of the Rabi model
• A hidden analytic structure of the Rabi model
• Solving two-mode squeezed harmonic oscillator and $k$th-order harmonic generation in Bargmann-Hilbert spaces
• How to calculate spectra of Rabi and related models

Cited by in corpus (1)

• Analytic solutions of the Teukolsky equation for massless perturbations of any spin in de Sitter background