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Dynamical properties of a two-level atom in three variants of the two-photon \(q\)-deformed Jaynes-Cummings model. (English) Zbl 1065.81629

Summary: Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three variants of the two-photon \(q\)-deformed Jaynes-Cummings model. The model is based on the generalized deformed oscillator algebra, \([\widehat A,\widehat A^+]=(\widehat N+1)f^2(\widehat N+1)-\widehat Nf^2(\widehat N)\) in which \(f(\widehat N)\) as a function of number operator \(\widehat N\) determines not only the intensity dependence of atom-field coupling, when the model Hamiltonian is expressed in terms of non-deformed field operators, but also the structure of initial state of the radiation field. With the field initially being in three different types of \(q\)-deformed coherent states, each of them corresponding to a particular form of the function \(f(\widehat N)\), the quantum collapse and revival effects as well as atomic dipole squeezing are studied for both on- and off-resonant atom–field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures, which are absent in the non-deformed Jaynes-Cummings model, and the magnitude of dipole squeezing may be increased.

MSC:

81V80 Quantum optics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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