  We propose to apply stimulated adiabatic passage to transfer atoms from their
ground state into Rydberg excited states. Atoms a few micrometers apart
experience a dipole-dipole interaction among Rydberg states that is strong
enough to shift the atomic resonance and inhibit excitation of more than a
single atom. We show that the adiabatic passage in the presence of this
interaction between two atoms leads to robust creation of maximally entangled
states and to two-bit quantum gates. For many atoms, the excitation blockade
leads to an effective implementation of collective-spin and
Jaynes-Cummings-like Hamiltonians, and we show that the adiabatic passage can
be used to generate collective Jx=0 eigenstates and Greenberger-Horne-Zeilinger
states of tens of atoms.
