Stochastic initiation of superradiance in a cavity: Decoherence through pseudospin exchange

We study superradiance from a fully inverted medium in the presence of two channels for atomic relaxation. Spontaneous emission from individual atoms is included and competes with the collective emission responsible for superradiance. We compare exact results within the quantum trajectory formalism with a previous approximation [J. P. Clemens and H. J. Carmichael, Phys. Rev. A 65, 023815 (2002)] which neglects the reexcitation of an atom after it spontaneously emits. The approximation underestimates the decoherence during the second half of an emitted pulse.