Quadratic Lie algebras and quasiexact solvability of the two-photon Rabi Hamiltonian

Articles you may be interested inOn the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations Two-photon spectroscopy of the (n,3s) Rydberg transition in acetaldehyde: The torsional sequence This paper is concerned with the rigorous analytical determination of the spectrum of the two-photon and the two-mode quantum Rabi models. To reach this goal, we exploit the hidden symmetries in these models by means of the unitary and similarity transformations in addition to the Bargmann-Fock space description. In each case, the purely quantum mechanical problem of the Rabi model studied is reduced to solutions for differential equations. This eventually gives a third-order differential equation for each of these models, which is reduced to a second-order differential equation by additional transformations. The analytical expressions of the wave functions describing the energy levels are obtained in terms of the confluent hypergeometric functions. C 2014 AIP Publishing LLC. [http://dx.

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“…(36). Let us mention that this result does agree with those presented in earlier works, see, for example, Refs.…”

Section: Spectrum Of the Two-photon Rabi Hamiltoniansupporting

confidence: 93%

“…7,9,20,21,24,36, and 38 for some works). Specifically, the energy levels obtained in our paper may be compared to those obtained in Refs.…”

Section: Discussionmentioning

confidence: 99%

Full spectrum of the two-photon and the two-mode quantum Rabi models

Dossa

Avossevou

2014

Journal of Mathematical Physics

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“…It is also known that the parameters of the two-photon Rabi model are restricted by |4g| < ω, otherwise the eigenfunctions are not normalizable [5,6].…”

Section: Introductionmentioning

confidence: 99%

Solvability of the two-photon Rabi Hamiltonian

2012

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Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of standard (one-photon) Rabi Hamiltonian, published by Braak in Phys. Rev. Lett. 107, 100401 (2011). The Hamiltonian is rewritten as a set of two differential equations. Symmetries that get hidden after further treatment are found. One can plainly see, how the Hilbert space splits into four disjunct subspaces, categorized by four values of the symmetry parameter c = ±1, ±i. There were only two values ±1 for the standard Rabi model. Four analytic functions are introduced by a recurrence scheme for the coefficients of their series expansion. All their roots yield the complete spectrum of the Hamiltonian. Eigenstates in Bargmann space are also at disposal.

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“…Its spectrum collapses into a continuous band for a specific value of the coupling strength [42][43][44][45]. In the transition from the strong to the USC regime of the twophoton Rabi model, a continuous symmetry breaks down into a four-folded discrete symmetry, identified by a generalized-parity operator [46].…”

Section: Introductionmentioning

confidence: 99%

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

et al. 2017

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The controllability of current quantum technologies allows to implement spin-boson models where two-photon couplings are the dominating terms of light-matter interaction. In this case, when the coupling strength becomes comparable with the characteristic frequencies, a spectral collapse can take place, i.e. the discrete system spectrum can collapse into a continuous band. Here, we analyze the thermodynamic limit of the two-photon Dicke model, which describes the interaction of an ensemble of qubits with a single bosonic mode. We find that there exists a parameter regime where two-photon interactions induce a superradiant phase transition, before the spectral collapse occurs. Furthermore, we extend the mean-field analysis by considering second-order quantum fluctuations terms, in order to analyze the low-energy spectrum and compare the critical behavior with the one-photon case.

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Quadratic Lie algebras and quasiexact solvability of the two-photon Rabi Hamiltonian

Abstract: It is proved that the two-photon Rabi Hamiltonian is quasi exactly solvable on the basis of the two different quadratic Lie algebras.

Cited by 20 publications

References 16 publications

Full spectrum of the two-photon and the two-mode quantum Rabi models

Full spectrum of the two-photon and the two-mode quantum Rabi models

Solvability of the two-photon Rabi Hamiltonian

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

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