Exact density matrix for the degenerate-Raman-coupled model in the presence of collisions

Exact expressions are obtained for the density matrix in the operator form and for the quasiprobabilities for the system of an atom undergoing Raman transitions between two degenerate levels on interaction with a quantized field in a lossy cavity driven by an external field. The model is generalized to include the effects of atomic dephasing collisions. The spectral properties of the radiation are discussed, and the equation of motion of the density matrix is derived in the presence of collisions and an external drive. The equation is found to be of second order with respect to time in the absence of the driving field and also analytically solvable.