Spin squeezing of atoms by Rydberg blockade

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We show that the interaction between Rydberg atomic states can provide continuous spin squeezing of atoms with two ground states. The interaction prevents the simultaneous excitation of more than a single atom in the sample to the Rydberg state, and we propose to utilize this blockade effect to realize an effective collective spin hamiltonian Jₓ²-Jy². With this hamiltonian the quantum mechanical uncertainty of the spin variable Jₓ+Jy can be reduced significantly.