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Physica A Statistical Mechanics and its Applications

New optical equations for the interaction of a two-level atom with a single mode of the electromagnetic field

A. Sãndulescu, Eliade N. Stefanescu

Published Dec 1, 1989• 11 citations
Publisher
DOI
10.1016/0378-4371(89)90440-8

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A new method is devised to study the atomic inversion in the model of a two-level atom interacting with a single quantized mode of the (initially coherent) electromagnetic field in an ideal resonant cavity. The method is based on number-theoretic results applied to the approximation of special series, specifically, on the functional equation for Jacobi theta functions and the ATS theorem. New asymptotic formulas are derived, with the help of which the behavior of the atomic inversion function on various time intervals can be determined in detail depending on the parameters of the system.

Computational Mathematics and Mathematical Physics•Nov 1, 2017•1 citation
In the framework of a general theory of open quantum systems, we obtain a quantum master equation for the two-level atom interacting with a single mode of the electromagnetic field. On this basis, we obtain new optical equations. In comparison with the conventional Bloch-Feynman optical equations which contain three phenomenological parameters, the new equations contain nine phenomenological parameters. New physical effects , due to the opening of the system, are predicted: 1) a resonance frequency shift, 2) an asymmetry of the spectral line, 3) a modification of the dependence of the absorbtion coefficient and of the nonlinear dephasing on the atomic detuning, and 4) an additional nonlinear dependence of the absorbtion coefficient on the electric field. For a rather small atom density when the fourth effect can be neglected,we found an analytical expression of the transmittivity characteristic of an optical bistable Fabry-Perot resonator and found a good agreement with the experiment.
We consider NNN driven two-level atoms interacting with a structured reservoir. By dressing the collective operators within a semiclassical approach, we derive a master equation and a mean-field single-particle effective Hamiltonian. This Hamiltonian describes the optical bistability phenomenon occurring in the relation between an input electromagnetic field and the effective output generated by the NNN atoms. The dissipative part of the master equation and the effective single-particle Hamiltonian contain new terms due the reservoir structure of modes. In plotting the output field amplitude and phase, for a structured reservoir, as a function of the input amplitude, one verifies the bistable behavior in both. We illustrate our results for two structured reservoirs: one having a Lorentzian shape for the distribution of modes, and the second is modeled as a photonic band-gap structure.
A new method is devised to study the atomic inversion in the model of a two-level atom interacting with a single quantized mode of the (initially coherent) electromagnetic field in an ideal resonant cavity. The method is based on number-theoretic results applied to the approximation of special series, specifically, on the functional equation for Jacobi theta functions and the ATS theorem. New asymptotic formulas are derived, with the help of which the behavior of the atomic inversion function on various time intervals can be determined in detail depending on the parameters of the system.