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Register a new userThe asymmetric quantum Rabi model in the polaron picture
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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 $epsilon$ is smaller than the harmonic frequency $omega$, such an overweighted anti-polaron can occur beyond a critical value of the coupling strength $g$; if $epsilon$ 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.
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We employ a polaron picture to investigate the properties of the two-photon quantum Rabi model (QRM), which describes a two-level or spin-half system coupled with a single bosonic mode by a two-photon process. In the polaron picture, the coupling in the two-photon process leads to spin-related asymmetry so that the original single bosonic mode splits into two separated frequency modes for the opposite spins, which correspond to two textit{bare} polarons. Furthermore, the tunneling causes these two bare polarons to exchange their components with each other, thus leading to additional textit{induced} polarons. According to this picture, the variational ground-state wave function of the two-photon QRM can be correctly constructed, with the ground-state energy and other physical observables in good agreement with the exact numerics in all the coupling regimes. Furthermore, generalization to multiple induced polarons involving higher orders in the tunneling effect provides a systematic way to yield a rapid convergence in accuracy even around the difficult spectral collapse point. In addition, the polaron picture provides a distinctive understanding of the spectral collapse behavior, that is about the existence of discrete energy levels apart from the collapsed spectrum at the spectral collapse point. This work illustrates that the polaron picture is helpful to capture the key physics in this nonlinear light-matter interaction model and indicates that this method can be applicable to more complicated QRM-related models.
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.
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 Schrodinger potentials on the line. This leads to particular QES Poschl-Teller potentials. The complete spectral equivalence is then established between the AQRM and generalised Poschl-Teller potentials. This result extends a previous mapping between the symmetric quantum Rabi model and a QES Poschl-Teller potential. The complete spectral equivalence between the two systems suggests that the physics of the generalised Poschl-Teller potentials may also be explored in experimental realisations of the quantum Rabi model.
We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters in the regimes of interest where the squeezing effect becomes negligible. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state, and make a comparison with existing approximations and the exact solution. The results show that the variational expansion is a significant improvement over the existing approximations for the AQRM.
In this paper, we derive the symmetry operators ($J$s) in the asymmetric two-photon quantum Rabi models in terms of Bogoliubov operator approaches. $ J^2$ can be expressed as a polynomial in terms of the Hamiltonian, which uncovers the $mathbb{Z}_{2}$ nature of the hidden symmetry in this two-photon model rigorously. The previous symmetry operators in the asymmetric one-photon quantum Rabi models are reproduced readily in terms of Bogoliubov operator approaches, and the obtained operators are expressed much more concisely. It is found that the polynomial degree of $J^2$ in the two-photon model is twice of that in the one-photon model.
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