  Conditions to achieve an unusually strong Rydberg spin-exchange interaction
are investigated and proposed as a means to generate pairwise entanglement and
realize a SWAP-like quantum gate for neutral atoms. Ground-state entanglement
is created by mapping entangled Rydberg states to ground states using optical
techniques. A protocol involving SWAP gate and pairwise entanglement operations
is predicted to create global entanglement of a chain of $N$ atoms in a time
that is independent of $N$.

Quantum Physics;Atomic Physics