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Entanglement and purity loss for the system of two 2-level atoms in the presence of the Stark shift

H. A. Hessian, Mostafa Hashem

Published Dec 7, 2010• 11 citations
Publisher

Abstract

In this paper, we have presented an analytic solution for two 2-level identical atoms interacting with a single-mode quantized radiation field, taking into account the level shifts produced by Stark shift. We assume that the two atoms are initially prepared in the exited state and the field in a coherent state. We investigate the purity loss of the system and bipartite partitions of the system. The effects of the Stark shift on the purity loss of the system and different bipartite partitions of the system (field-two atoms, atom-(field+atom)) through the tangles are considered. In particular, the effect of the Stark shift on the amount of entanglement between atoms and field is evaluated by the negativity.

DOI
10.1007/s11128-010-0210-1

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In this paper, we have presented an analytic solution for two 2-level identical atoms interacting with a single-mode quantized radiation field, taking into account the level shifts produced by Stark shift. We assume that the two atoms are initially prepared in the exited state and the field in a coherent state. We investigate the purity loss of the system and bipartite partitions of the system. The effects of the Stark shift on the purity loss of the system and different bipartite partitions of the system (field-two atoms, atom-(field+atom)) through the tangles are considered. In particular, the effect of the Stark shift on the amount of entanglement between atoms and field is evaluated by the negativity.
We considered a quantum model consisting of two effective two-level atoms interacting with a single-mode thermal cavity field through two-photon transitions. We explored the entanglement dynamics between two atoms, and studied the effect of the Stark shift on the entanglement. The results showed that for a separable initial atomic state the Stark shift enhances the amount of atom-atom entanglement induced by the thermal field. For entangled atomic state the Stark shift reduces the the atom-atom entanglement oscillations.
In this paper, we investigated the dynamics of atomic entanglement in a quantum system consisting of two identical two-level atoms (qubits) resonantly interacting with a mode of a thermal cavity field through degenerate two-photon transitions, in the presence of a Stark energy level shift. An analytical expression is obtained for the atom entanglement (negativity) parameter for separable and entangled initial states of atoms. The influence of the Stark shift on the degree of atom-atom entanglement is considered. It is established that the Stark shift leads to a significant increase in the degree of atom entanglement in the case of separable initial states of atoms and to stabilization of atomic entanglement in the case of entangled initial states of atoms.
In this manuscript, we study a new non-linear system which represents a ?-type five level atom interacting with a quantized four-mode electromagnetic field. A non-linear Stark shift is introduced, through the elimination of intermediate levels (two and four) using the adiabatic elimination technique. By using the Schrodinger equation we obtain the analytic solution this model. Some statistical aspects through the effective Hamiltonian are presented such as the collapses-revivals phenomenon, degree of purity, concurrence, and the squeezing phenomenon with respect to study the effect of Stark shift parameters on these statistical aspects. For small values of the Stark shift parameter, the collapse times increase and the atomic inversion symmetry axis shifts upward, while the entanglement decreases significantly. It has been noted that the system is affected by the Stark shift parameter.
Considering two-atom degenerate two-photon Tavis-Cummings model, we investigate the entanglement between two atoms prepared initially in the coherent disentangled states and cavity field prepared in few-photon Fock state, and study the effect of the Stark shift on entanglement. The results show that the atom–atom negativity evolve periodically with time and the periods are affected by the Stark shift and initial coherent atomic state and that the atom–atom entanglement can be greatly enhanced due to the presence of Stark shift. We also have shown that entanglement sudden death effect vanishes for some parameters of the considered system due to the presence of Stark shift. In addition, the entanglement sudden death effect vanishes due to the presence of Stark shift. We have derived that the dynamic Stark shift can be used to control entanglement between two initially disentangled atoms.