Spin squeezing and Schr\"{o}dinger cat generation in atomic samples with Rydberg blockade

A scheme is proposed to prepare squeezed states and Schr\"{o}dinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser fields, we can suppress non-adiabatic transfer under the time varying Hamiltonian and significantly speed up the evolution towards a maximally squeezed, J_z=0, collective spin state.