The asymmetric quantum Rabi model and generalised Poschl-Teller potentials

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 Schrödinger potentials on the line. This leads to particular QES Pöschl–Teller potentials. The complete spectral equivalence is then established between the AQRM and generalised Pöschl–Teller potentials. This result extends a previous mapping between the symmetric quantum Rabi model and a QES Pöschl–Teller potential. The complete spectral equivalence between the two systems suggests that the physics of the generalised Pöschl–Teller potentials may also be explored in experimental realisations of the quantum Rabi model.This work is also supported by the Australian Research Council through grant DP170104934