The asymmetric quantum Rabi model and generalised Pöschl-Teller potentials

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 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.

arXiv comment17 pages, 4 figures, minor changes, additional references

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• Spectral Collapse in the two-photon quantum Rabi model
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• Attempt to find the hidden symmetry in the asymmetric quantum Rabi model
• Generalized adiabatic approximation to the quantum Rabi model
• Squeezed displaced entangled states in the quantum Rabi model
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• The Yang-Baxter paradox