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Journal of Mathematical Physics

An investigation of entanglement and quasiprobability distribution in a generalized Jaynes-Cummings model

Mahmoud Abdel‐Aty

Published Mar 20, 2003• 38 citations
Publisher

Abstract

In this paper, we consider a unified approach to study the degree of entanglement of two-level systems interacting with a quantized electromagnetic field. We investigate a range of parameters in a generalized Jaynes–Cummings model (JC-model) with intensity-dependent, field nonlinearity and nonresonant coupling. In terms of the density matrix and without the diagonal approximation we derive an explicit expression for the entanglement degree using a function analogous to mutual entropy. This notion is inspired by the fact that the quantum state may be interpreted as a measure of information. With the aid of the quasiprobability distribution function, the statistical properties of the field are analyzed. It is shown that when the atom is initially in its upper-level and the one-photon at resonance, the Q-function splits into two peaks and counter rotate in phase space.

DOI
10.1063/1.1559643

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In this paper, we consider a unified approach to study the degree of entanglement of two-level systems interacting with a quantized electromagnetic field. We investigate a range of parameters in a generalized Jaynes–Cummings model (JC-model) with intensity-dependent, field nonlinearity and nonresonant coupling. In terms of the density matrix and without the diagonal approximation we derive an explicit expression for the entanglement degree using a function analogous to mutual entropy. This notion is inspired by the fact that the quantum state may be interpreted as a measure of information. With the aid of the quasiprobability distribution function, the statistical properties of the field are analyzed. It is shown that when the atom is initially in its upper-level and the one-photon at resonance, the Q-function splits into two peaks and counter rotate in phase space.
We extend our earlier investigations ( Furuichi S and Abdel-Aty M 2001 J. Phys. A: Math. Gen. 34 6851 ) on the entanglement degree of a two-level atom to include any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We present a derivation of the unitary operator within the frame of the dressed state approach, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. The influences of the nonlinearity, Stark shifts and detuning on the degree of entanglement are examined. It is shown that features of the degree of entanglement are influenced significantly by the kinds of nonlinearity of the single-mode field. The model presented in this paper can be regarded as a generalization of the Jaynes-Cummings model.
In this paper, by using the notion of negativity, we study the degree of entanglement of a two-level atom interacting with a quantized radiation field, described by the Jaynes–Cummings model (JCM). We suppose that initially the field is in a pure state and the atom is in a general mixed state. In this case the negativity fully captures the entanglement of the JCM. We investigate the case that the initial state of the field is a coherent state. The influences of the detuning on the degree of entanglement are also examined.
In this paper, a model in which two moving atoms interact with a two-mode field with nondegenerate two-photon transitions is studied in the presence of intensity-dependent coupling. To discuss the entanglement dynamics between subsystems as well as nonclassicality of the system, the time-dependent form of the state vector of the system is exactly obtained. The dynamics of entanglement between the atoms and the field is evaluated by the von Neumann entropy. To examine the degree of entanglement between the atoms, concurrence and negativity are obtained. Then, in order to understand the nonclassicality feature of the state vector of the system, the two-mode Wigner–Weyl quasi-probability distribution function is precisely derived. It is deduced from the numerical results that the domain and the maximum amount of the degree of entanglement and nonclassicality of the system can be appropriately tuned by suitably adopting the nonlinearity function and the field-mode structure parameters.
We present a mathematical procedure which leads us to obtain analytical solutions for the atomic inversion and Wigner function in the framework of the Jaynes–Cummings model with an external quantum field, for any kind of cavity and driving fields. Such solutions are expressed in the integral form, with their integrands having a common term that describes the product of the Glauber–Sudarshan quasiprobability distribution functions for each field, and a kernel responsible for the entanglement. Considering two specific initial states of the tripartite system, the formalism is then applied to calculate the atomic inversion and Wigner function where, in particular, we show how the detuning and amplitude of the driving field modify the entanglement. In addition, we also obtain the correct quantum-mechanical marginal distributions in phase space.
The Jaynes-Cummings model (JCM) of a two-level atom interacting with a quantized radiation field has been investigated theoretically. Of particular interest is the transition of a quantized electromagnetic field of the model to a classical one in the limit of very large average photon number. In this thesis, two aspects of the JCM are examined. Firstly, it is shown that, in contrast to the general case, for specic initial atom-field states, there is exact correspondence between the atomic inversion predicted by the JCM and that predicted by the semiclassical model in which the field is treated classically from the outset. Secondly, the degree of quantum entanglement of the JCM is investigated quantitatively and it is shown that, at any nite absolute temperature greater than zero, the atom and field are never separable and the degree of quantum entanglement approaches zero in the high and low temperature limits
We have studied the influences of the Stark shifts and a Kerr-like medium on the degree of entanglement and the spectrum, for a system in which a two-level atom interaction occurs with a single mode of an electromagnetic field two-photon processes. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. It is shown that the Stark shift effect changes the quasiperiod of the field entropy and, hence, the entanglement between the particle and the field.