  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.
