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.

Generalized adiabatic approximation to the quantum Rabi model

“…Instead, only the level crossing points in the spectrum can be determined through finite-term constraint polynomials of system parameters [30,31]. For this reason, the QRM is also referred to as quasi-solvable [32][33][34]. These isolated solutions are called Juddian points, and the determining polynomials have been derived via different approaches [5,16,35,36].…”

Squeezed displaced entangled states in the quantum Rabi model

“…that interpolates between the so-called degenerate qubit, ω 0 = 0, and relativistic, ω = 0, regimes for the extremal values of the control parameter δ ∈ [0, 1]. We recover the QRM for Strictly speaking, our model is solvable [8,33]. We focus on the regimes with analytic closed form solution and favour the Fulton-Gouterman procedure to diagonalize it in the…”

The Yang-Baxter paradox

“…These include algebraic [57], analytic [49], functional [27], thermodynamic [56], offdiagonal [13], double-row transfer matrix constructions [53], and by using separation of variables [52]. Moreover there are other techniques available to yield exact solutions, such as the Jordan-Wigner transform [36], those used in Kitaev-type models [33,64], and those used in Rabi-type models [12,31,45,65]. These somewhat confuse attempts to provide an unambiguous definition for what constitutes exact-solvability, and to identify its relationship to integrability.…”