Eur. Phys. J. Plus (2014) 129: 193
https://doi.org/10.1140/epjp/i2014-14193-0

Regular Article

The interaction between a single two-level atom and the combination of a frequency converter and the sub-harmonic generation

¹ Mathematics Department, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
² Mathematics Department, Faculty of Science, Al-Azhar University, 11884, Nasr City, Cairo, Egypt

^* e-mail: m.sebaweh@physics.org

Received: 9 April 2014
Revised: 13 July 2014
Accepted: 14 July 2014
Published online: 12 September 2014

Abstract

The problem of a time-dependent quantum system, which consists of coupled sub-harmonic generation with the parametric down conversion injected within a single cavity containing an atom, is considered. The problem is transformed into the interaction between the su(1,1) quantum system and a single two-level atom. The wave function is calculated and the expectation values for the dynamical operators are obtained. It is shown that the phenomenon of collapses and revivals are sensitive to the variation of the Bargmann index k and the Perelomov parameter η; moreover, a coherent trapping behavior is seen at the atomic coherence angle θ = π/2. The phenomena of bunching and anti-bunching are reported where the atomic angle θ and the phase angle φ as well as η are the most effective parameters. They are also effective for the variance squeezing, however the Bargmann index k increases the fluctuations and decreases the amount of squeezing. For the linear entropy we have observed that the index k has no effect, but the main effective parameters are θ, φ and η in addition to the ratio between the atomic frequency and the coupling parameter.