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Physica A Statistical Mechanics and its Applications

Statistical properties of two-mode parametric amplifier interacting with a single atom

A.‐S. F. Obada, M. Sebawe Abdalla, Eied Mahmoud Khalil

Published Feb 2, 2004• 26 citations
Publisher
DOI
10.1016/j.physa.2003.12.036

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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.

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Noisy parametric amplifiers in non-equilibrium thermo field dynamics

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Single-mode and two-mode parametric amplifiers under the influence of Markovian environments are studied by means of non-equilibrium thermo field dynamics. In the presence of both parametric coupling and system–environment interaction, the dissipative Heisenberg equations of motion are solved for the optical modes of interest. By making use of the solutions, it is examined whether the noisy parametric amplifiers can exhibit the non-classical properties. Furthermore, it is shown that the two-mode parametric amplifier is equivalent to the two single-mode parametric amplifiers with subsequent beam splitting, even if they are influenced by the environments.

Journal of Modern Optics•Jun 26, 2014•1 citation
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.
Single-mode and two-mode parametric amplifiers under the influence of Markovian environments are studied by means of non-equilibrium thermo field dynamics. In the presence of both parametric coupling and system–environment interaction, the dissipative Heisenberg equations of motion are solved for the optical modes of interest. By making use of the solutions, it is examined whether the noisy parametric amplifiers can exhibit the non-classical properties. Furthermore, it is shown that the two-mode parametric amplifier is equivalent to the two single-mode parametric amplifiers with subsequent beam splitting, even if they are influenced by the environments.