Some Nonclassical Effects of Two Three-Level Atoms Interacting with SU (1) Quantum System
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Journal of Russian Laser Research, Volume 41, Number 5, September, 2020
SOME NONCLASSICAL EFFECTS OF TWO THREE-LEVEL ATOMS INTERACTING WITH SU (1,1) QUANTUM SYSTEM A.-S. F. Obada,1 M. M. A. Ahmed,1 M. A. El-Deberky,2 and R. N. Rabea2∗ 1 Mathematics
Department Faculty of Science Al-Azher University Nasr City 11884, Cairo, Egypt 2 Mathematics
Department Faculty of Science (Girls Branch) Al-Azher University Nasr City 11884, Cairo, Egypt ∗ Corresponding
author e-mail:
rabei.rash @ azhar.edu.eg
Abstract We consider the interaction between two three-level atoms in the Ξ configuration and a quantum system described through SU (1, 1) group algebra operators. To study the quantum phenomena and underlying dynamical behavior, we calculate the wave function of the system. In particular, we investigate collapse and revival phenomena, the correlation function, and the Husimi quasidistribution Q-function.
Keywords: two three-level atoms, SU (1, 1) quantum system, correlation function, Q-function.
1.
Introduction
The interaction between field and matter lies at the heart of physics. In the field of quantum optics, the Jaynes–Cummings model (JCM) is one of the most important models, where this interaction is quantum-mechanically treated [1]. The model simply describes the interaction between a two-level atom and a single mode of the radiation field; it has been generalized subsequently in many different directions. Various extensions of the JCM and further nonclassical effects have been studied and investigated [2]. These extensions include one or two atoms [3, 4] involving two or three levels with one or two cavity-field modes undergoing single-photon or multiphoton processes [5–7]. The quantum properties of a V -type, Λ-type, and Ξ-type three-level atoms have been studied [8, 9]. The time evolution operator for the N level atom and (N − 1) multiphoton modes has been calculated [10]. In experiments, the strong coupling regime was shown to be present in a solid-state system, in addition to the observation of a coherent interaction in a superconducting two-level system with a single microwave photon [11]. Lie groups generated by operators of a simple algebra, such as su(2) and su(1, 1) and their simple generalizations, have been used to describe and study different aspects in quantum optics [12]. The generators of the Lie group form the basis of its Lie algebra. The annihilation and creation operators aa well as the number operators are the cornerstones in the realization of the Heisenberg–Weyl algebra [13]. Manuscript submitted by the authors in English on July 29, 2020. c 2020 Springer Science+Business Media, LLC 1071-2836/20/4105-0459
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Journal of Russian Laser Research
Volume 41, Number 5, September, 2020
Their eigenstates and the coherent states [12, 14] can be easily constructed. The familiar algebras of some Lie groups have been used to construct several coherent states [15]; well-known ones include the Perelomov coherent states [16], the Barut–Gerradillo coherent states [17], and the intelligent states [18]. The in
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