Entanglement of large atomic samples: a Gaussian state analysis

We present a Gaussian state analysis of the entanglement generation between two macroscopic atomic ensembles due the continuous probing of collective spin variables by optical Faraday rotation. The evolution of the mean values and the variances of the atomic variables is determined and the entanglement is characterized by the Gaussian entanglement of formation (GEoF) and the logarithmic negativity. The effects of induced opposite Larmor rotation of the samples and of light absorption and atomic decay are analyzed in detail.