The hidden symmetry of the asymmetric two-photon Rabi model

Xie, You-Fei; Chen, Qing-Hu

doi:10.48550/arxiv.2106.05817

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…Note added. The preliminary symmetry operators of the asymmetric tpQRM for low biases = 2β and 4β was given in our unpublished work [47]. Interestingly, the same idea was used to derive the lowest symmetry operator in the asymmetric two-mode QRM most recently [48].…”

Section: Discussionmentioning

confidence: 99%

Symmetry operators of the asymmetric two-photon quantum Rabi model

Xie¹,

Chen²

2022

J. Phys. A: Math. Theor.

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The true level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) have been observed when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Generally, such level crossings imply the existence of the hidden symmetry because the bias term breaks the obvious symmetry exactly. In this work, we propose a Bogoliubov operator approach (BOA) for the asymmetric tpQRM to derive the symmetry operators associated with the hidden symmetry hierarchically. The explicit symmetry operators consisting of Lie algebra at low biases can be easily obtained in our general scheme. We believe the present approach can be extended for other asymmetric Rabi models to ﬁnd the relevant hidden symmetry.

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Section: Discussionmentioning

confidence: 99%

Symmetry operators of the asymmetric two-photon quantum Rabi model

Xie¹,

Chen²

2022

J. Phys. A: Math. Theor.

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“…Note that in asymmetric tmQRM, [J (1) ] 2 depends on q. But in the asymmetric two-photon QRM [46], it is independent of q. [J (1) ] 2 is a quadratic polynomial in H tm in (50).…”

Section: Hidden Symmetry Operator For Asymmetric Two-mode Qrmmentioning

confidence: 99%

Analytical solution and hidden symmetry operators of asymmetric two-mode quantum Rabi model

Zhang¹,

Xia²,

Li³

et al. 2022

J. Phys. A: Math. Theor.

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The asymmetric two-mode QRM breaks Z2-symmetry and also implies hidden symmetry. In this paper, the energy spectrum are analytically computed with Bogoliubov transformation and su(1,1) Lie algebra. The analytical results are in good agreement with those obtained by numerical calculation. We identify the condition for the bias parameter such that level crossings appear in the spectrum which are caused by the hidden symmetry. This condition is related not only to the field frequency, but also to the coupling strength between the field and qubit. The level crossing points could be determined by the pole energy and recurrence coefficients. This is tested and verified in the low energy levels. The generators of the hidden Z2-symmetry, commuting with the Hamiltonian, are derived within the Bogoliubov operator approach. The present results may provide more information to the hidden symmetry in the asymmetric two-mode QRM.

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“…However, the practical approaches for a general expression of the symmetry operators at arbitrary large integer biases are still lacking, and would be very challenging within the framework of the Fock space [16,20]. By the BOA scheme [24], the symmetry operators for low order symmetry operators for both one-and two-photon AQRMs have been derived rigorously in an elegant way [26]. In this work, we will propose a general scheme to find symmetry operators relevant to the hidden symmetry in the one-photon AQRM with the BOA.…”

Section: Introductionmentioning

confidence: 99%

General symmetry operators of the asymmetric quantum Rabi model

Xie,

Chen

2021

Preprint

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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 symmetry of the asymmetric two-photon Rabi model

Cited by 3 publications

References 29 publications

Symmetry operators of the asymmetric two-photon quantum Rabi model

Symmetry operators of the asymmetric two-photon quantum Rabi model

Analytical solution and hidden symmetry operators of asymmetric two-mode quantum Rabi model

General symmetry operators of the asymmetric quantum Rabi model

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