Quantum Trajectory Analysis of the Two-Mode Three-Level Atom Microlaser
  We consider a single atom laser (microlaser) operating on three-level atoms interacting with a two-mode cavity. The quantum statistical properties of the cavity field at steady state are investigated by the quantum trajectory method which is a Monte Carlo simulation applied to open quantum systems. It is found that a steady state solution exists even when the detailed balance condition is not guaranteed. The differences between a single mode microlaser and a two-mode microlaser are highlighted. The second-order correlation function g^2(T) of a single mode is studied and special attention is paid to the one-photon trapping state, for which a simple formula is derived for its correlation function. We show the effects of the velocity spread of the atoms used to pump the microlaser cavity on the second-order correlation function, trapping states, and phase transitions of the cavity field. 
Tarek A. Elsayed, Abdulaziz Aljalal