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Journal of Modern Optics

Generation of a nonlinear two-mode Stark shift through the adiabatic elimination method

A.‐S. F. Obada, Eied Mahmoud Khalil, M. M. A. Ahmed

Published Apr 27, 2006• 26 citations
Publisher

Abstract

In this contribution a three-level atom in interaction with a two-mode quantized electromagnetic field, initially prepared in an entangled two-mode coherent state is considered. Through the elimination of an intermediate level by using the adiabatic elimination method a nonlinear Stark shift is introduced. Exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects through the effective two-level atom interacting with the mode through multiphotons with the Stark shift are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing. It has been shown that the system is sensitive to any change in the parameter representing the Stark shift. General conclusions reached are illustrated by numerical results.

DOI
10.1080/09500340600551440

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In this contribution a three-level atom in interaction with a two-mode quantized electromagnetic field, initially prepared in an entangled two-mode coherent state is considered. Through the elimination of an intermediate level by using the adiabatic elimination method a nonlinear Stark shift is introduced. Exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects through the effective two-level atom interacting with the mode through multiphotons with the Stark shift are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing. It has been shown that the system is sensitive to any change in the parameter representing the Stark shift. General conclusions reached are illustrated by numerical results.
In this contribution, a three level atom in interaction with a two-mode quantized electromagnetic field, initially prepared in an entangled two-mode coherent state, is considered. Through the elimination of an intermediate level using the adiabatic elimination method, a nonlinear Stark shift is introduced. The exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects through the effective two-level atom interacting with the two-mode and multiphotons processess with the nonlinear Stark shift are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing and variance squeezing. It has been shown that the system is sensitive to any change in the parameter representation of the Stark shift. General conclusions reached are illustrated by numerical results.
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.
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.
Using the adiabatic elimination we have managed to deal with the problem of the interaction between a single three-level atom and |NNN| two-level non-interacting atoms. The adiabatic elimination is used to obtain the effective Hamiltonian that describes a nonlinear interaction in the form of a Stark-like shift between a two-level atom and su|(2)N(2)N(2)N| two-level atoms. The time evolution operator is calculated in the presence of a Stark-like shift and the detuning parameters. The time-dependent wave function is determined through the evolution operator and consequently the density matrix is obtained. We adopt an initial wave function for the |NNN| two-level atoms that takes into account the structural degeneracies occurring in the system and thus generalize the atomic coherent state. The phenomenon of the collapses and revivals of the atomic population inversion for different values of the Stark shift parameters is considered. The degree of entanglement is also investigated and discussed, where the linear entropy is used. Finally we examine the variance squeezing for the system for different values of the involved parameters. It is shown that different values of the Stark shift parameters lead to different observations of the squeezing in the quadratures.
We consider a two-mode quantized field described in a coherent state interacting with a four-level atom. An effective Hamiltonian is obtained by adiabatically eliminating the intermediate two levels in a cascade process. The influence of the Stark shifts on the atomic inversion is examined, as well as on the second order auto-correlation function and on the cross-correlation between the field modes. The results of the calculations are illustrated numerically.   Key word: Adiabatic elimination, Stark-shift, second order auto-correlation function, cross-correlation between the field modes.