Asymmetric Quantum Rabi Model Research Articles

The asymmetric quantum Rabi model and generalised Pöschl–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.

Asymptotic behavior of observables in the asymmetric quantum Rabi model

The asymmetric quantum Rabi model with broken parity invariance shows spectral degeneracies in the integer case, that is when the asymmetry parameter equals an integer multiple of half the oscillator frequency, thus hinting at a hidden symmetry and accompanying integrability of the model. We study the expectation values of spin observables for each eigenstate and observe characteristic differences between the integer and noninteger cases for the asymptotics in the deep strong coupling regime, which can be understood from a perturbative expansion in the qubit splitting. We also construct a parent Hamiltonian whose exact eigenstates possess the same symmetries as the perturbative eigenstates of the asymmetric quantum Rabi model in the integer case.

Symmetry of asymmetric quantum Rabi models

The aim of this paper is a better understanding for the eigenstates of the asymmetric quantum Rabi model by Lie algebra representations of . We define a second order element of the universal enveloping algebra of , which, through the action of a certain infinite dimensional representation of , provides a picture of the asymmetric quantum Rabi model equivalent to the one drawn by confluent Heun ordinary differential equations. Using this description, we prove the existence of level crossings in the spectral graph of the asymmetric quantum Rabi model when the symmetry-breaking parameter ϵ is equal to , and conjecture a formula that ensures likewise the presence of level crossings for general . This result on level crossings was demonstrated numerically by Li and Batchelor in 2015, investigating an earlier empirical observation by Braak (2011). The first analysis of the degenerate spectrum was given for the symmetric quantum Rabi model by Kuś in 1985. In our picture, we find a certain reciprocity (or -symmetry) for if the spectrum is described by representations of . We further discuss briefly the non-degenerate part of the exceptional spectrum from the viewpoint of infinite dimensional representations of having lowest weight vectors.

The asymmetric quantum Rabi model in the polaron picture

The concept of the polaron in condensed matter physics has been extended to the Rabi model, where polarons resulting from the coupling between a two-level system and single-mode photons represent two oppositely displaced oscillators. Interestingly, tunneling between these two displaced oscillators can induce an anti-polaron, which has not been systematically explored in the literature, especially in the presence of an asymmetric term. In this paper, we present a systematic analysis of the competition between the polaron and anti-polaron under the interplay of the coupling strength and the asymmetric term. While intuitively the anti-polaron should be secondary owing to its higher potential energy, we find that, under certain conditions, the minor anti-polaron may gain a reversal in the weight over the major polaron. If the asymmetric amplitude ϵ is smaller than the harmonic frequency ω, such an overweighted anti-polaron can occur beyond a critical value of the coupling strength g; if ϵ is larger, the anti-polaron can even be always overweighted at any g. We propose that the explicit occurrence of the overweighted anti-polaron can be monitored by a displacement transition from negative to positive values. This displacement is an experimentally accessible observable, which can be measured by quantum optical methods, such as balanced Homodyne detection.