Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

TL;DR

This paper provides an exact spectral analysis of the anisotropic two-photon Rabi model using a novel algebraic approach, revealing its connection to quantum phase transitions in many-body systems.

Contribution

It introduces a new exact method based on Bogolubov rotation for analyzing the spectrum of the anisotropic two-photon Rabi model, applicable also to two-modes Rabi models.

Findings

Spectrum characterized by a meromorphic function

Model exhibits features similar to quantum phase transitions

Applicable to two-modes Rabi models with shared algebraic structure

Abstract

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying $su(1,1)$ Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions.