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Journal of Scientific Research in Science /Journal of Scientific Research in Science

The interaction between a Three-Level Atom and Four Systems of N-Two Level Atoms

Mohamed Shehata, S. S. Ibrahim, M. H. Osman, N. N. Nagib, A. T. M. Makram-Allah, M. M. A. Ahmed, D. A. M. Abo-Kahla

Published Feb 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.21608/jsrs.2020.129796

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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.
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.
We investigate some new aspects of the nonlinear interaction between a three-level Ξ-type atom and bimodal field. The photon-assisted atomic phase damping, detuning parameter, Kerr nonlinearity and the time-dependent coupling have been considered. The general solution has been obtained by using the Schrődinger equation when the atom and the field are initially prepared in the excited state and coherent state, respectively. The atomic population inversion and concurrence are discussed. It is shown that the time-dependent coupling parameter and the detuning parameter can be considered as quantum controller parameters of the atomic population inversion and quantum entanglement in the considered model.
In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.
Quantum Control of the Time-Dependent Interaction between a Three-Level ΞΞΞ-Type Atom and a Two-Mode Field with Damping Term
The purpose of this paper is to investigate some properties through a three-level ΞΞΞ-type atom interacting with a two-mode field. We test this system in the presence of the photon assisted atomic phase damping, detuning parameter and Kerr nonlinearity. Also, the coupling parameter modulated to be time-dependent. The problem solution of this model is given by using the Schrődinger equation when the atom and the field are initially prepared in the excited state and coherent state, respectively. We used the results to calculate some aspects such as atomic population inversion and concurrence. The results show that the time-dependent coupling parameter and the detuning parameter can be considered as a quantum control parameters of the atomic population inversion and quantum entanglement in the considered model.
In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.