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Resonance

Analysis of Atomic Entanglement in Three-mode Jaynes—Cummings Model for Different Field Statistics

Amrita Amrita, Rohit Singh, Aprajita Krishna, Kavita Verma

Published Dec 1, 2021• 0 citations
Publisher
DOI
10.1007/s12045-021-1280-3

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In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz
Dynamics of atom–field correlations and single-mode nonclassicalities present in the resonant Jaynes–Cummings model are investigated using negativity and entanglement potential for a set of initial states. The study has revealed the interplay among three different types of nonclassicalities present in the model and established that the nonclassicality is continuously exchanged between the field and atom through atom–field correlations. Further, it is observed that the entanglement potential does not capture all single-mode nonclassicality, and there exists some residual nonclassicality in the reduced single-mode states at the output of the beam splitter that is not captured by the entanglement in which single-mode nonclassicality is quantitatively mapped in Asboth’s criterion. Additional layers of beam splitters are added to deplete all the nonclassicality and to reveal that almost all residual nonclassicality is captured with three layers of beam splitters. Further, the reduced states of the atom and field have zero (non-zero) quantum coherence in the Fock basis when the atom–field correlations are maximum if the field (or atom) has zero (non-zero) quantum coherence initially.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.