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Journal of Russian Laser Research

Quantum Statistical Aspects of Interactions Between the Radiation Field and Two Entangled Two-Level Atoms in the Presence of Stark Shift Terms

Eman M. A. Hilal, Eied Mahmoud Khalil

Published May 1, 2018• 6 citations
Publisher
DOI
10.1007/s10946-018-9710-8

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The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.
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.
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.