N Two-Level Atoms in a Driven Optical Cavity: Quantum Dynamics of Forward Photon Scattering for Weak Incident Fields  Robert J. Brecha (U. Dayton), Perry Rice, and M. Xiao (U. Arkansas)  Phys. Rev. A 59, .2392-2417  (1999).

We consider the driven Tavis-Cummings model with losses: a system composed of N two-level atoms coupled to a single-field mode. Both cavity loss and spontaneous emission to non-cavity modes are included, as well as a driving field. With both a driving field and dissipation present, the system attains a non-trivial steady-state.

In the weak-field limit, we derive results for the second-order correlation function g⁽²⁾(t). Several nonclassical effects are observed: photon antibunching, sub-Poissonian counting
statistics, and a novel effect where g⁽²⁾(t) vanishes at a non-zero correlation time. Previous cavity QED effects, such as spontaneous emission rate modification and "vacuum" Rabi splitting can be understood in terms of an inherently classical model: coupled harmonic oscillators. The results presented here can be given no classical interpretation. Our results are interpreted in terms of quantum interference between probability amplitudes for diffferent scattering processes. The reduced density operator for the atom-cavity system factorizes for weak fields, and hence one can describe the system by a pure-state, even in the presence of dissipation.

We also use a linearized Fokker-Planck approach to the same problem that requires a system-size expansion based on the premise that the system has a large number of atoms and/or photons. The results of this calculation are compared to those obtained by the pure-state formlism for small systems, in an effort to understand the limits of the Fokker-Planck approach for small systems.