  Resonant laser excitation of multiple Rydberg atoms are prohibited, leading
to Rydberg blockade, when the long-range van der Waals interactions are
stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e.
simultaneous excitation of more than one Rydberg atoms, by off-resonant laser
excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise
to strongly correlated many-body dynamics and spin-orbit coupling, and also
finds quantum computation applications. Instead of commonly used van der Waals
interactions, we investigate antiblockade dynamics of two Rydberg atoms
interacting via dipole-dipole exchange interactions. We study typical
situations in current Rydberg atoms experiments, where different types of
dipole-dipole interactions can be achieved by varying Rydberg state couplings.
Effective Hamiltonian governing underlying antiblockade dynamics is derived. We
illustrate that geometric gates can be realized with the Rydberg antiblockade
which is robust against decay of Rydberg states. Our study may stimulate new
experimental and theoretical exploration of quantum optics and strongly
interacting many-body dynamics with Rydberg antiblockade driven by
dipole-dipole interactions.
