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Journal of Quantum Information Science

The Pancharatnam Phase of a Three-Level Atom Coupled to Two Systems of N-Two Level Atoms

D. A. M. Abo-Kahla

Published Jan 1, 2016• 7 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 effects of the quantum numbers and the coupling parameters between spins on the Pancharatnam phase and the atomic inversion, for some special cases of the initial states, are investigated. The comparison between the two effects shows that the analytic results are well consistent.

DOI
10.4236/jqis.2016.61006

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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 effects of the quantum numbers and the coupling parameters between spins on the Pancharatnam phase and the atomic inversion, for some special cases of the initial states, are investigated. The comparison between the two effects shows that the analytic results are well consistent.
In this paper, we study the interaction between a two-level atom and a three types of nonlinear interaction of two modes, two as a degenerate two photon and the third of the converter form. The solution to the Schrodinger equation is obtained exactly under a certain specific condition. By using this solution we discuss numerically the atomic inversion, the degree of entanglement through the atomic Wehrl entropy, the geometric phase entropy for chosen values of the detuning and coupling parameters. Statistical properties of the investigated system is discussed by the evolution of the Mandel parameter.
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.
In this article, the interaction between a time-dependent damping field and Λ-type of three-level atom is investigated. The effect of the atom and the fields' parameters on the behaviour of the atomic inversion, the generated entanglement between the atom and the cavity modes, the Pancharatnam geometric phase are discussed. It is shown that the phenomena of the collapses and revivals for the three physical quantities depend on the time-dependent coupling and the damping parameter. The long-lived behaviour of the non-classical correlation is observed either on the presence of only time-dependent coupling or at large values of the damping parameter. The damping effect has different features on the three phenomena, where the atomic inversion decays, the upper bounds of entanglement increases and increases periodic time of the Pancharatnam geometric phase.
We introduce the problem of three types of interaction between an N-level quantum system and a two-level atom where three coupling parameters are involved. The system can be deduced from the Heisenberg chain. The canonical transformation is used to remove two coupling parameters from the system and consequently it is reduced to atom–atom interaction. The wave function is calculated using the evolution operator and hence we have managed to obtain the expectation value of some dynamical operators. During our study of the atomic inversion we noted that the collapses period is shifted up when we take the effect of λ2 into consideration. While it is shifted up and down in the presence of λ3. The atomic angle plays a crucial role for controlling the degree of entanglement. For the variance squeezing we noted that the coupling parameter λ2 shows amounts of squeezing more than the case of λ3. Similar behavior is noted for the entropy squeezing.