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arXiv:quant-ph/0702101 · Physica Scripta

Negativity as entanglement degree of the Jaynes–Cummings model

Seyed Javad Akhtarshenas, M Farsi

Published Mar 8, 2007• 23 citations
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Abstract

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.

DOI
10.1088/0031-8949/75/5/003

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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.
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
The entanglement between an atom and field is investigated by using the Jaynes–Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r .
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.
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.
We investigated the entanglement of a quantum system consisting of a Jaynes-Cummings atom, thermal lossless cavity and an isolated atom. The analytical expressions of the atom-atom negativity for separable, separable coherent and entangled initial atomic states were obtained. The influence of initial atomic coherence, detuning between the atomic transition frequency and the field frequency and direct dipole-dipole interaction on an atom- atom entanglement is examined. We showed that for a separable and separable coherent initial atomic states a detuning might cause high atom-atom entanglement in the presence of the dipole-dipole interaction even for thermal field with high intensity. We also obtained that for entangled initial atomic states a detuning causes a stabilization of an entanglement oscillations.
The dissipation of the field in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels was studied. The initial degenerate atomic state affects the field coherence loss. When the degenerate atom is initially in an equal probability superposition state, the field coherence loss is smallest. It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field. When the degeneracy was considered, the coherence properties of the field could be affected by the reservoir qualitatively, if a nonlinear two-photon process is involved. This is different from the dissipation of one-photon JCM with degenerate atomic levels.