  We propose a scheme for controlling interactions between Rydberg-excited
neutral atoms in order to perform a fast high-fidelity quantum gate. Unlike
dipole-blockade mechanisms already found in the literature, we drive resonantly
the atoms with a state-dependent excitation to Rydberg levels, and we exploit
the resulting dipole-dipole interaction to induce a controlled atomic motion in
the trap, in a similar way as discussed in recent ion-trap quantum computing
proposals. This leads atoms to gain the required gate phase, which turns out to
be a combination of a dynamic and a geometrical contribution. The fidelity of
this scheme is studied including small anharmonicity and temperature effects,
with promising results for reasonably achievable experimental parameters.
