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arXiv:0708.2532 · Journal of Physics A Mathematical and General

Relationship between the atomic inversion and Wigner function for multimode multiphoton Jaynes–Cummings model

Faisal A. A. El-Orany

Published May 25, 2004• 16 citations
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Abstract

In this paper we consider the multimode multiphoton Jaynes–Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with N modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase-space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of initial atomic states as well as moving atoms. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for the Wigner function.

DOI
10.1088/0305-4470/37/23/013

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In this paper we consider the multimode multiphoton Jaynes–Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with N modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase-space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of initial atomic states as well as moving atoms. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for the Wigner function.
In this paper, we study the evolution of two two-level atoms interacting with a single-mode quantized radiation field, namely, the two-atom multiphoton Jaynes–Cummings model (JCM). We assume that the field and the atoms are initially prepared in the superposition of displaced number states and excited atomic states, respectively. For this system, we investigate the atomic inversion, Wigner function, phase distribution and entanglement. We show that for symmetric (asymmetric) atoms, the system can generate asymmetric (symmetric) cat states at a quarter of the revival time. Furthermore, the degrees of entanglement for the field–atoms and the one-atom–remainder tangles depend on the rate of energy flow between the parties. The interference in phase space decreases the degree of entanglement in the bipartite.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.
One of the most significant physical models for characterizing the dynamics of robust-intensity and strong laser fields, has recently been solved using the so-called multiphoton Jaynes–Cummings model. This generalized model describes the interaction between a two-level atom and a field in the presence of multiple photons simultaneously. In the present study, we consider the generalized form of the equation, known as the fractional equation. An exact fractional solution of the multiphoton Jaynes–Cummings model is derived. Furthermore, the non-Gaussianity of the system is examined using the Wigner and Husimi quasiprobability distributions. Our main result can be summarized as follows: although the initial state is taken as a direct product of the atomic and coherent states, the system remains non-Gaussian when fractional dynamics is taken into account. The results show that the Wigner function consistently exhibits negative regions for small values of the fractional order, corresponding to strong fractional memory. Moreover, it is demonstrated that both the Wigner and Husimi functions are highly sensitive to variations in the parameters of the multiphoton Jaynes–Cummings model. In particular, localization of the quantum state is observed in both functions within a specific region of the phase plane.
In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.
In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.