English

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

Quantum Physics 2018-07-09 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1804.03878,
  title  = {The asymmetric quantum Rabi model and generalised P\"oschl-Teller potentials},
  author = {Kai-Long Guan and Zi-Min Li and Clare Dunning and Murray T Batchelor},
  journal= {arXiv preprint arXiv:1804.03878},
  year   = {2018}
}

Comments

17 pages, 4 figures, minor changes, additional references