Two-photon parametric pumping versus two-photon absorption: A quantum jump approach

We show that it is possible to produce superpositions of distinct coherent states (even or odd coherent states) in a cavity where the field is pumped by two-photon parametric amplification and simultaneously undergoes two-photon absorption by a beam of three-level atoms that travel through the cavity interacting with the cavity field. Previous studies modeled the absorber with an effective Hamiltonian without involving real atomic excitation or entanglement, a procedure justified only for weak coupling of the two-photon absorbing atoms. We examine the validity of this assumption by modeling the atomic absorber dynamics from the onset. In order to study the system numerically we make use of a Monte Carlo wave-function method in which the two-photon absorbing atoms can interact with the cavity and evolve with large Rabi angles.