Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian

TL;DR

This paper demonstrates that the two-photon Rabi Hamiltonian is quasi-exactly solvable by leveraging two distinct quadratic Lie algebras, providing new insights into its algebraic structure.

Contribution

It introduces a novel approach to solving the two-photon Rabi Hamiltonian using quadratic Lie algebras, advancing the understanding of its solvability.

Findings

Two different quadratic Lie algebras underpin the quasi-exact solvability.

The algebraic structure enables explicit solutions for parts of the spectrum.

The approach offers a new perspective on the algebraic methods in quantum optics.

Abstract

It is proved that the two-photon Rabi Hamiltonian is quasi exactly solvable on the basis of the two different quadratic Lie algebras.