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Journal of Modern Optics

Dynamics of the Jaynes-Cummings model in the presence of photonic crystals

Ali A. Kamli, Smail B. Bougouffa

Published Apr 1, 2002• 1 citation
Publisher

Abstract

The three-level atom Jaynes-Cummings model is solved exactly and its dynamics investigated in photonic crystals that exhibit band gaps. The atom-field coupling and the probability amplitudes are evaluated as functions of the mode frequency and for different cavity parameters. Besides band-gap effects, the system exhibits novel local field effects. These show as peaks in the atom-field coupling and hence peaks or dips in the probability functions.

DOI
10.1080/09500340110109016

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The three-level atom Jaynes-Cummings model is solved exactly and its dynamics investigated in photonic crystals that exhibit band gaps. The atom-field coupling and the probability amplitudes are evaluated as functions of the mode frequency and for different cavity parameters. Besides band-gap effects, the system exhibits novel local field effects. These show as peaks in the atom-field coupling and hence peaks or dips in the probability functions.
The dynamics of the Q-function for a two-level system coupled to one-cavity mode (Jaynes-Cummings model) in the presence of a Kerr-like medium is investigated. Starting the field mode in a coherent state and the atom in its upper state, the Q-function splits into distinct distribution functions as in the case of the Jaynes-Cummings model. In addition to this splitting the Kerr medium introduces an additional rotation and broadening of the counter-rotating contributions to the Q-function. It is further shown that the discrete superpositions of coherent states produced by the Kerr medium split into additional peaks is due to atomic coupling.