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Zhang, YZ; Zhang, YZ (reprint author), Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia.; Zhang, YZ (reprint author), Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.
On the 2-mode and k-photon quantum Rabi models
Source PublicationREVIEWS IN MATHEMATICAL PHYSICS
Language英语
KeywordQuasi-exactly Solvable Systems Rabi Model And Extensions Bargmann-hilbert Spaces
AbstractBy mapping the Hamiltonians of the 2-mode and 2-photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wave functions in the Bargmann-Hilbert spaces only if the frequency. and coupling strength g satisfy certain constraints. This is in sharp contrast to the quantum Rabi model for which entire wave functions always exist. For model parameters fulfilling the aforesaid constraints, we determine transcendental equations whose roots give the regular energy eigenvalues of the models. Furthermore, we show that for k >= 3, the k-photon Rabi model does not possess wave functions which are elements of the Bargmann-Hilbert space for all non-trivial model parameters. This implies that the k >= 3 case is not diagonalizable, unlike its RWA cousin, the k-photon Jaynes-Cummings model which can be completely diagonalized for all k.
2017
Volume29Issue:4Pages:1750013
Subject AreaPhysics
DOIhttp://dx.doi.org/10.1142/S0129055X17500131
Funding OrganizationAustralian Research Council [DP140101492] ; Australian Research Council [DP140101492] ; Australian Research Council [DP140101492] ; Australian Research Council [DP140101492]
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Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/22069
Collection理论物理所科研产出_SCI论文
Corresponding AuthorZhang, YZ (reprint author), Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia.; Zhang, YZ (reprint author), Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Zhang, YZ,Zhang, YZ ,Zhang, YZ . On the 2-mode and k-photon quantum Rabi models[J]. REVIEWS IN MATHEMATICAL PHYSICS,2017,29(4):1750013.
APA Zhang, YZ,Zhang, YZ ,&Zhang, YZ .(2017).On the 2-mode and k-photon quantum Rabi models.REVIEWS IN MATHEMATICAL PHYSICS,29(4),1750013.
MLA Zhang, YZ,et al."On the 2-mode and k-photon quantum Rabi models".REVIEWS IN MATHEMATICAL PHYSICS 29.4(2017):1750013.
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