Analytical Solutions to Asymmetric Two-Photon Rabi Model

TL;DR

This paper derives nearly exact analytical solutions for an asymmetric two-photon Rabi model using the Bethe ansatz within the Segal-Bargmann representation, advancing understanding of complex quantum interactions.

Contribution

It introduces a method to obtain nearly exact solutions for a generalized asymmetric two-photon Rabi model using a Bethe ansatz approach.

Findings

Solutions in exact analytical form for the fourth-order differential equation.

Applicable to arbitrary states and specific parameter restrictions.

Provides a new analytical framework for complex quantum models.

Abstract

Within the Segal-Bargmann representation, a generalized Rabi model is considered that includes both two-photon and asymmetric terms. It is shown that, through a suitable transformation, nearly exact solutions can be obtained using the Bethe ansatz approach. Applying this approach to the meromorphic structure of the resulting differential equation, solutions in exact analytical form of the fourth-order problem are presented for both an arbitrary state and for the restriction between the parameters.