Spin squeezing of atoms by the dipole interaction in virtually excited Rydberg states

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 significantly reduced.