Resonance of geometric quantities and hidden symmetry in the asymmetric Rabi model

Yu, Qinjing; Lü, Zhiguo

doi:10.1103/physreva.108.052214

Cited by 1 publication

(2 citation statements)

References 67 publications

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“…Since π 2 /8 ≈ 1.2337 this gives almost a perfect agreement of the approximation (18) with the data, further supporting the notion that the order of the oscillatory term in theorem 2.1 is the best possible and that order of the error term may be improved. In figure 15, we illustrate the spectral curves for the AQRM for different values of ϵ ⩾ 0.…”

Section: Spacing Distribution For Fixed Paritysupporting

confidence: 70%

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Spacing distribution for quantum Rabi models ^*

Thi Hoai Nguyen,

Reyes-Bustos,

Braak

et al. 2024

J. Phys. A: Math. Theor.

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The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z 2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

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Section: Spacing Distribution For Fixed Paritysupporting

confidence: 70%

“…Recently, geometric phases and dynamics of the AQRM have been investigated as well as its semi-classical variant [18]. The flip term given by the bias parameter ϵ in the AQRM breaks the natural Z 2 (= Z/2Z) or 'parity' symmetry which is characteristic for the QRM and renders it integrable [19].…”

Section: Introductionmentioning

confidence: 99%

Spacing distribution for quantum Rabi models ^*

Thi Hoai Nguyen,

Reyes-Bustos,

Braak

et al. 2024

J. Phys. A: Math. Theor.

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Resonance of geometric quantities and hidden symmetry in the asymmetric Rabi model

Cited by 1 publication

References 67 publications

Spacing distribution for quantum Rabi models ^*

Spacing distribution for quantum Rabi models ^*

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Resonance of geometric quantities and hidden symmetry in the asymmetric Rabi model

Cited by 1 publication

References 67 publications

Spacing distribution for quantum Rabi models *

Spacing distribution for quantum Rabi models *

Contact Info

Product

Resources

About

Spacing distribution for quantum Rabi models ^*

Spacing distribution for quantum Rabi models ^*