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Register a new userGeneral symmetry operators of the asymmetric quantum Rabi model within Bogoliubov operator approach
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In this paper, we propose a general scheme to obtain the symmetry operators in the asymmetric quantum Rabi model within Bogoliubov operator approaches. The previous symmetry operators for small integer biases can be extremely easily reproduced in our scheme. Moreover, we can easily obtain the symmetry operators for arbitrary large biases hierarchically, which is perhaps hardly treated with the standard approach based on the expansions on the original Fock space.
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The hidden $mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) has recently been revealed via a systematic construction of the underlying symmetry operator. Based on the AQRM result, we propose an ansatz for the general form of the symmetry operators for AQRM-related models. Applying this ansatz we obtain the symmetry operator for three models: the anisotropic AQRM, the asymmetric Rabi-Stark model (ARSM) and the anisotropic ARSM.
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.
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.
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.
The asymmetric quantum Rabi model (AQRM) has a broken $mathbb{Z}_2$ symmetry, with generally a non-degenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the $mathbb{Z}_2$-symmetric quantum Rabi model are recovered, however, without any obvious parity-like symmetry. This unknown symmetry has thus been referred to as hidden symmetry in the literature. Here we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunnelling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunnelling.
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