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Journal of the Egyptian Mathematical Society

Some studies of the interaction between N-two level atoms and three level atom

D. A. M. Abo-Kahla, M. M. A. Ahmed

Published Dec 15, 2015• 6 citations
Publisher

Abstract

In this paper, we present the analytical solution for the model that describes the interaction between a three level atom and two systems of N-two level atoms. The effect of the quantum numbers on the atomic inversion and the purity, for some special cases of the initial states, are investigated. We observe that the atomic inversion and the purity change remarkably by the change of the quantum numbers.

DOI
10.1016/j.joems.2015.10.004

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In this paper, we present the analytical solution for the model that describes the interaction between a three level atom and two systems of N-two level atoms. The effect of the quantum numbers on the atomic inversion and the purity, for some special cases of the initial states, are investigated. We observe that the atomic inversion and the purity change remarkably by the change of the quantum numbers.
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We have four systems, each of them contains N-atoms, and each atom of them consists of two levels, and all of them interact with an atom consisting of three levels. Moreover, the atom is also related to the systems by coupling parameters that are time-dependent. By considering particular conditions, the exact solution for the wave function is realized. Then we survey the atomic population inversion in addition to the normalized correlation functions. We examine the influence of many parameters on the previous statistical aspects. We deduce from the conclusions that the behavior of the correlation function is affected by the existence of the time-dependent coupling parameters between spins. We prove that changing the values of the coupling parameters between spins λk, the parameters ε, and the quantum numbers Nγ enables us to control the correlated behavior in addition to the atomic population. So, we can control this model through these parameters.
We have four systems, each of them contains N-atoms, and each atom of them consists of two levels, and all of them interact with an atom consisting of three levels. Moreover, the atom is also related to the systems by coupling parameters that are time-dependent. By considering particular conditions, the exact solution for the wave function is realized. Then we survey the atomic population inversion in addition to the normalized correlation. We examine the influence of many parameters on the previous statistical aspects. We deduce from the conclusions that the behavior of the correlation function is affected by the existence of the time-dependent coupling parameters between spins. We prove that changing the values of the coupling parameters between spins λk, the parameters ε, and the quantum numbers Nγ enables us to control the correlated behavior in addition to the atomic population. So, we can control this model through these parameters.