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arXiv:quant-ph/0402195 · Journal of the Physical Society of Japan

Dynamical Properties of a Two-Level Atom in Three Variants of the Two-Photonq-Deformed Jaynes–Cummings Model

M. H. Naderi, M. Soltanolkotabi, R. Roknizadeh

Published Sep 15, 2004• 33 citations
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Abstract

Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe 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 dipole squeezing may be enhanced.

DOI
10.1143/jpsj.73.2413

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Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe 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 dipole squeezing may be enhanced.
It is shown that various variants of the deformed Jaynes-Cummings model (JCM) correspond to the JCM with an intensity-dependent coupling characterized by two additional phenomenological parameters (p,q). The standard JCM is obtained for p=q=1. The quantum collapse and revival effects and the squeezing properties of a particular variant of the (p,q)-deformed Jaynes-Cummings model are studied numerically. The model is based on the q-deformed oscillator algebra ${\mathit{AA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$-${\mathit{qA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$A=1 that interpolates between Fermi-Dirac and Bose-Einstein statistics. If the cavity field is prepared initially in a q-deformed coherent state, the quantum collapse and revival effects are observed only for q\ensuremath{\approxeq}1. For q>1, the atomic inversion 〈${\mathrm{\ensuremath{\sigma}}}_{3}$(t)〉 exhibits chaoticlike behavior, which is a feature observed also in other q-deformed JCM's. Strong squeezing is observed only for small positive and small negative q values. If q\ensuremath{\approxeq}1, the squeezing is very weak. In the limit q=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\varepsilon} with \ensuremath{\varepsilon}\ensuremath{\ll}1, the algebra can be interpreted as describing a small violation of Bose-Einstein statistics in the JCM.
A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes–Cummings model (JCM) is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.
The aim of this study is to investigate an effective two-level atom coupled to a twomode f-deformed cavity field with and without the rotating wave approximation.The first section discusses the theoretical model of the interaction between a two-mode cavity-field and an effective two-level atom within the framework of an f-DJCM without the rotating wave approximation.After that, we obtain the reduced density matrix of the atom with and without the rotating-wave approximation.Then, we have investigated the effect of the counterterm on temporal evolution of various nonclassical properties of the atom, i.e., atomic population inversion, atomic dipole squeezing and atom-field entanglement.Particularly, we compare the numerical result for three different values of the deformation parameter q (q=1, q=1.1, q=1) with and without the rotating wave approximation.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
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
The dynamics of the driven Jaynes-Cummings model where a two-level atom is coupled to a single mode of cavity fields and is driven by an external coherent field is investigated. We find that in this model quantum collapse and revivals of the atomic population inversion and squeezing of the cavity field can be generated from a thermal photon state. We also notice that the squeezing is very sensitive to the mean number of thermal photons initially in the cavity, but the quantum collapse and revivals are not. The influence of the amplitude of the driving field and various detuning parameters on the nonclassical effects is discussed. The result shows that one can use the external field to control nonclassical effects in the Jaynes-Cummings model.