Exact Floquet solutions in a Parity-Time-Symmetric Rabi Model

TL;DR

This paper reveals that a PT-symmetric Rabi model has a hidden algebraic structure allowing for exact solutions at spectral phase transition points, linking model parameters to resonance conditions.

Contribution

It demonstrates the existence of quasi-exact solutions in a PT-symmetric Rabi model through hidden $sl(2)$ symmetry, specifically at exceptional points.

Findings

Exact solutions located at spectral exceptional points

Hidden $sl(2)$ symmetry identified in the model

Parameter constraints interpreted as resonance conditions

Abstract

It is shown that a semiclassical Rabi model with parity-time (PT) symmetry has a hidden $sl(2)$ symmetry and hence possesses quasi-exact solutions. These are located precisely at the exceptional points of the spectrum, the boundaries of the PT-symmetric phase. The corresponding constraints on the model parameters can be interpreted as a resonance relationship between the constant and periodic driving terms.