We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic field and the two-level atom depends on the field intensity. Upon modeling the matter–radiation coupling through the Holstein–Primakoff realization of algebra su(1,1), we evaluate first- and second-order eigenenergies and eigenstates both in the weak-coupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the first case, among various effects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the su(1,1)-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.

The su(1,1)-like intensity-dependent Rabi model: A perturbative analysis of weak and strong-coupling regimes / Penna, Vittorio; Raffa, Francesco Antonino. - In: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION. - ISSN 0219-7499. - STAMPA. - 12:(2014), pp. 1560010-1-1560010-10. [10.1142/S0219749915600102]

The su(1,1)-like intensity-dependent Rabi model: A perturbative analysis of weak and strong-coupling regimes

PENNA, Vittorio;RAFFA, Francesco Antonino
2014

Abstract

We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic field and the two-level atom depends on the field intensity. Upon modeling the matter–radiation coupling through the Holstein–Primakoff realization of algebra su(1,1), we evaluate first- and second-order eigenenergies and eigenstates both in the weak-coupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the first case, among various effects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the su(1,1)-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2601563
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