Modeling Collective Emission in Cavities by Phase Space Trajectories

We model N electronic two-level systems (TLSs) coupled to a multimode cavity by sampling independent trajectories in Wiger phase space with a Meyer-Miller-Stock-Thoss (MMST) mapping Hamiltonian. We show that this approach can not only provide us an intuitive physical interpretation of quantum electrodynamics (i.e. sampling electronic and photonic zero-point energies in phase space represents radiative self-interaction and vacuum fluctuations respectively), but also correctly describe many intriguing collective emission phenomena, including spontaneous emission for an array of TLSs in the singly excited manifold, Dicke's superradiance and subradiance when all TLSs are excited, and even the quantum statistics for the delay time in superradiance. We also discuss possible further improvements of this approach.