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We propose to apply stimulated adiabatic passage to transfer atoms from theirground state into Rydberg excited states. Atoms a few micrometers apartexperience a dipole-dipole interaction among Rydberg states that is strongenough to shift the atomic resonance and inhibit excitation of more than asingle atom. We show that the adiabatic passage in the presence of thisinteraction between two atoms leads to robust creation of maximally entangledstates and to two-bit quantum gates. For many atoms, the excitation blockadeleads to an effective implementation of collective-spin andJaynes-Cummings-like Hamiltonians, and we show that the adiabatic passage canbe used to generate collective Jx=0 eigenstates and Greenberger-Horne-Zeilingerstates of tens of atoms.

Quantum gates and multi-particle entanglement by Rydberg excitation blockade and adiabatic passage