Regular Article

Analytical computation of nonclassical behavior for asymmetric two two-level atoms interacting with SU(1,1) quantum system

¹ Department of Mathematics,Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
² Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
³ Department of Mathematics, Faculty of Science, Al-Azhar University, 11884 Cairo, Egypt

^a e-mail: a.nahla@science.tanta.edu.eg

Received: 4 August 2018
Received in final form: 18 December 2018
Published online: 7 March 2019

Abstract

A quantum model of the asymmetric two two-level atoms interacting with the SU(1,1) quantum system is suggested. The rotating wave approximation (RWA) and the atom–atom interaction are considered in the Hamiltonian operator. The time-dependent wave function for asymmetric case is obtained analytically via solving the Schrödinger equation. Initially, the SU(1,1) quantum system is prepared in a Barut–Girardello coherent state and two atoms are in superposition states. Some of statistical properties of the proposed quantum model are calculated such as the atomic population inversion, the linear entropy as an indicator of entanglement degree, and the coherence degree by the second-order correlation function. Therefore, the nonclassical properties are discussed for different values of the initial atomic angles, the Barut–Girardello parameter, the Bargmann index and the detuning parameters. We note that the proposed quantum system is sensitive to the Barut–Girardello parameter and the Bargmann index. Moreover, there are nonclassical characteristics of the proposed system with the variation in the detuning parameters.