Exceptional and regular spectra of a generalized Rabi model

TL;DR

This paper analyzes the spectrum of a generalized Rabi model with different coupling strengths for co- and counter-rotating terms, revealing exceptional energy levels, quasi-exact solvability, and analytical spectrum approximations.

Contribution

It introduces the spectrum structure of a generalized Rabi model with explicit exceptional points and polynomial wave functions, extending understanding beyond the standard Rabi model.

Findings

Spectrum has regular and exceptional parts with crossing energy levels.

Exceptional states are described by finite polynomials satisfying Bethe ansatz equations.

In strong coupling, the spectrum forms two quasi-degenerate equidistant ladders.

Abstract

We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in a magnetic field with Rashba and Dresselhaus spin-orbit couplings. Like in case of the Rabi model, the spectrum of the generalized Rabi model consists of the regular and the exceptional parts. The latter is represented by the energy levels which cross at certain parameters' values which we determine explicitly. The wave functions of these exceptional states are given by finite order polynomials in the Bargmann representation. The roots of these polynomials satisfy a Bethe ansatz equation of the Gaudin type. At the exceptional points the model is therefore quasi-exactly solvable. An analytical approximation is derived for the regular part of the spectrum in the weak- and strong-coupling limits. In particular, in the strong-coupling limit the spectrum consists of two quasi-degenerate equidistant ladders.