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Acta Universitaria

Two-level atom in a cross cavity

J. C. García-Melgarejo, Javier J. Sanchez-Mondragon, Karla J. Sánchez Pérez, Omar S. Magaña‐Loaiza

Published Dec 6, 2013• 2 citations
Publisher

Abstract

In this work we propose a model to analyze the interaction of a two-level atom (TLA) placed in a cross cavity configuration interacting with two electromagnetic fields injected within the cavity. A canonical transformation for field operators is proposed to obtain ef­fective Hamiltonian such as that of Jaynes-Cummings and we calculate the wave function via time-evolution operator. We present results for the atomic inversion for a state in the weak intensity regime.

DOI
10.15174/au.2013.559

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In this work we propose a model to analyze the interaction of a two-level atom (TLA) placed in a cross cavity configuration interacting with two electromagnetic fields injected within the cavity. A canonical transformation for field operators is proposed to obtain ef­fective Hamiltonian such as that of Jaynes-Cummings and we calculate the wave function via time-evolution operator. We present results for the atomic inversion for a state in the weak intensity regime.
In this communication we handle a modified model representing the interaction between a two-level atom and two modes of the electromagnetic field in a cavity. The interaction between the modes is assumed to be of a parametric amplifier type. The model consists of two different systems, one represents the Jaynes–Cummings model (atom–field interaction) and the other represents the two mode parametric amplifier model (field–field interaction). After some canonical transformations the constants of the motion have been obtained and used to derive the time evolution operator. The wave function in the Schrödinger picture is constructed and employed to discuss some statistical properties related to the system. Further discussion related to the statistical properties of some physical quantities is given where we have taken into account an initial correlated pair-coherent state for the modes. We concentrate in our examination on the system behavior that occurred as a result of the variation of the parametric amplifier coupling parameter as well as the detuning parameter. It has been shown that the interaction of the parametric amplifier term increases the revival period and consequently longer period of strong interaction between the atom and the fields.