Dynamics of entanglement between two atomic samples with spontaneous scattering

We investigate the effects of spontaneous scattering on the evolution of entanglement of two atomic samples, probed by phase shift measurements on optical beams interacting with both samples. We develop a formalism of conditional quantum evolutions and present a wave function analysis implemented in numerical simulations of the state vector dynamics. This method allows to track the evolution of entanglement and to compare it with the predictions obtained when spontaneous scattering is neglected. We provide numerical evidence that the interferometric scheme to entangle atomic samples is only marginally affected by the presence of spontaneous scattering, and should thus be robust even in more realistic situations.