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

The asymmetric two-mode quantum Rabi model (tmQRM) breaks Z 2 -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 numeric...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-04, Vol.55 (15), p.155303
Main Authors: Yan, Zhanyuan, Xia, Yifei, Li, Jurihui, Ma, Jinying, Liu, Yan
Format: Article
Language:English
Subjects:
asymmetric two-mode Rabi model
hidden symmetry
level crossing
symmetry
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Summary:The asymmetric two-mode quantum Rabi model (tmQRM) breaks Z 2 -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 Z 2 -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 tmQRM.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac5a22