COLLECTIVE DECAY AS A STOCHASTIC-PROCESS

We apply two quantum-trajectory methods to a decaying system of N two- level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the tanh-like decay of th e inversion for large N. This tanh behavior is also found for the jump -free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emiss ion. However, we find that this behavior of superfluorescence is gover ned by the jump statistics. The jump-free evolution of the Dicke syste m displays other atypical behavior. We find that the energy of the sys tem can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffu sion method to the system, we find that the trajectories keep the syst em in a spin coherent state, which confirms the picture of superfluore scence for single trajectories as a toppling needle point. This enable s us to write an approximate analytic expression fbr the decay of the energy for any N. Finally, we discuss the calculation of two-time corr elation functions per trajectory and as an illustration we calculate t he single-trajectory spectra. In the quantum-jump method, these single -trajectory spectra do not correspond to intuition, which we ascribe t o the incompatibility of photon counting and spectral measurement.