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Optics Communications

Collapse and revival phenomena in the many-atom-jaynes-cummings model in the presence on initial fock- and coherent-state fields

JOSIP SEKE, Otto Hittmaır, Frank Rattay

Published Mar 1, 1989• 11 citations
Publisher
DOI
10.1016/0030-4018(89)90320-9

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The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
A complete description of the electric field in the Jaynes-Cummings model is presented using the exact operator solutions for the field variables. Two-time field correlation functions are calculated which display the destruction and subsequent partial revival of field coherence. It is shown that squeezing of the field can be enhanced for small n\ifmmode\bar\else\textasciimacron\fi{} when the atom is initially in a coherent superposition state. Amplitude-squared squeezing of both field quadratures occurs for all values of n\ifmmode\bar\else\textasciimacron\fi{} with these initial conditions. The squeezing is not related to collapse and revival phenomena.
We apply the concept of the mazer to the two-photon process and propose the idea of the two-photon mazer. We establish the general quantum theory of the two-photon mazer and calculate its emission probability in the special case of a mesa mode function. We study not only the case in which the cavity field is initially in a number state, but also the case in which the cavity field is initially in a coherent state. Under the condition of an initial coherent field, the emission probability shows the collapse-revival phenomena, which have different features in different regimes. In the thermal-atom regime, the collapse revivals are similar to that in the two-photon Jaynes-Cummings model. In the critical regime, the collapse revivals look like that in the one-photon Jaynes-Cummings model. In the ultracold-atom regime, the collapse revivals are different from those in the above two regimes. The reasons for these results have been analyzed.