  We report the generation of entanglement between two individual $^{87}$Rb
atoms in hyperfine ground states $|F=1,M=1>$ and $|F=2,M=2>$ which are held in
two optical tweezers separated by 4 $\mu$m. Our scheme relies on the Rydberg
blockade effect which prevents the simultaneous excitation of the two atoms to
a Rydberg state. The entangled state is generated in about 200 ns using pulsed
two-photon excitation. We quantify the entanglement by applying global Raman
rotations on both atoms. We measure that 61% of the initial pairs of atoms are
still present at the end of the entangling sequence. These pairs are in the
target entangled state with a fidelity of 0.75.
