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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Jaynes-Cummings model of an indirect gap semiconductor cavity

Jose Maria Escalante, Alejandro Martı́nez

Published Apr 10, 2012• 1 citation
Publisher

Abstract

In this work, we present a Jaynes-Cummings model of an indirect bandgap semiconductor engineered to confine simultaneously photons and phonons (acousto-optical cavity). From our theoretical analysis, the typical collapse-revival behavior is obtained. Finally, we get an analytical approximate expression of Rabi frequency in such a system.
DOI
10.1117/12.921079

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The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.
The effects of counter-rotating terms (CRTs) on Rabi splitting and the dynamic evolution of atomic population in the Jaynes—Cummings model are studied with a coherent-state approach. When the coupling strength increases, the Rabi splitting becomes of multi-Rabi frequencies for the initial state of an excited atom in a vacuum field, and the collapses and revivals gradually disappear, and then reappear with quite good periodicity. Without the rotating-wave approximation (RWA), the initial excited state contains many eigenstates rather than two eigenstates under the RWA, which results in the multi-peak emission spectrum. An analytical approximate solution for the strong coupling regime is obtained, which gives a new oscillation frequency and explains the recovery of collapses and revivals due to the equal energy spacing.
The position as well as the width of the atomic wave packet passing through an optical cavity may affect the matter-field interaction. As a result, the internal dynamics of a two-level atom, such as the Rabi oscillations or the collapse and revival phenomenon, may be strongly modified with respect to the standard Jaynes-Cummings model. In particular, for a sufficiently large spread of the atomic position, the atomic population inversion displays the characteristic ringing behavior of the Bessel function J0{\mathit{J}}_{0}J0​ differently from the usual full Rabi oscillation.