Dynamics of formation of superposition states of light in an absorbing medium

The process of simultaneous absorption of two photons in a medium in the presence of a weak one-photon absorption is considered. The medium is perturbed from outside in a two-photon parametric manner. The formation of a stationary even-parity superposition state of light in such a medium is shown to be possible in the region of small amplitudes of the state (weak perturbations of the system). This is associated with the fact that, in this region of interaction, the field spends considerably more time in the even superposition state than in the odd state. It is shown that a nonstationary superposition state of light with a large amplitude of the state (large photon numbers) can be obtained for interaction times that are longer than the most probable time of the first two-photon quantum jump of the field state and shorter than the most probable time of the first one-photon jump of the field state. The dynamics of formation of the quantum entropy of the field is studied by numerical simulation of quantum trajectories of the system. The Wigner functions of the state of the field are calculated. Analytical results are obtained for the density matrix of the stationary state of the system in the presence of a weak one-photon absorption.