Comparison of quantum-state diffusion and quantum-jump simulations of two-photon processes in a dissipative environment

Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schr\"odinger ``cat'' states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.