The asymmetric quantum Rabi model and generalised P\"oschl-Teller potentials

TL;DR

This paper establishes a spectral equivalence between the asymmetric quantum Rabi model and generalized P"oschl-Teller potentials, extending previous mappings and suggesting experimental exploration of these potentials through quantum Rabi systems.

Contribution

It introduces a complete spectral equivalence between the AQRM and generalized P"oschl-Teller potentials, expanding the understanding of their relationship beyond symmetric cases.

Findings

Spectral equivalence between AQRM and QES hyperbolic potentials

Extension of previous symmetric model mapping to asymmetric case

Potential for experimental realization of generalized P"oschl-Teller physics

Abstract

Starting with the Gaudin-like Bethe ansatz equations associated with the quasi-exactly solved (QES) exceptional points of the asymmetric quantum Rabi model (AQRM) a spectral equivalence is established with QES hyperbolic Schr\"odinger potentials on the line. This leads to particular QES P\"oschl-Teller potentials. The complete spectral equivalence is then established between the AQRM and generalised P\"oschl-Teller potentials. This result extends a previous mapping between the symmetric quantum Rabi model and a QES P\"oschl-Teller potential. The complete spectral equivalence between the two systems suggests that the physics of the generalised P\"oschl-Teller potentials may also be explored in experimental realisations of the quantum Rabi model.