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Optics Communications

Two-photon revival-collapse phenomenon in the evolution of the quadrature squeezing of the four-photon Jaynes–Cummings model

Faisal A. A. El-Orany

Published Feb 4, 2006• 2 citations
Publisher
DOI
10.1016/j.optcom.2006.01.029

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In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in l -photon coherent states. This system is described by a two-mode multiphoton (i.e., k 1 , k 2 ) Jaynes–Cummings model (JCM). For this system we investigate the occurrence of the revival–collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for ( k 1 , k 2 ) = (3,1) provides RCP similar to that of the atomic inversion of the case ( k 1 , k 2 ) = (1,1); however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case ( k 1 , k 2 ) = (2,2) provides information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.
In this paper we study the interaction between two-level atom and quantized single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival-collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three-photon (standard) JCM provided that the initial photon-number distribution of the radiation has a smooth envelope.