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Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

M. Sebaweh Abdalla

Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

E-mail Address: m.sebaweh@physics.org

Corresponding author.

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E. M. Khalil

Mathematics Department, Faculty of Science, Taif University, Taif City 888, Saudi Arabia

Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

E-mail Address: eiedkhalil@yahoo.com

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, and

A.-S. F. Obada

Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

E-mail Address: asobada@yahoo.com

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https://doi.org/10.1142/S0217979217502113Cited by:3 (Source: Crossref)

Abstract

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.

Keywords:

PACS: 32.80.−t, 42.50.Ct, 03.65.Ud, 03.65.Yz

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Vol. 31, No. 15

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History

Received 9 January 2017

Revised 3 May 2017

Accepted 4 May 2017

Published: 24 May 2017

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

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Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

Abstract

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