  With the recent production of polar molecules in the quantum regime,
long-range dipolar interactions are expected to facilitate the understanding of
strongly interacting many-body quantum systems and to realize lattice spin
models for exploring quantum magnetism. In atomic systems, where interactions
require wave function overlap, effective spin interactions on a lattice can be
realized via superexchange; however, the coupling is weak and limited to
nearest-neighbor interactions. In contrast, dipolar interactions exist in the
absence of tunneling and extend beyond nearest neighbors. This allows coherent
spin dynamics to persist even at high entropy and low lattice filling. Effects
of dipolar interactions in ultracold molecular gases have so far been limited
to the modification of chemical reactions. We now report the observation of
dipolar interactions of polar molecules pinned in a 3D optical lattice. We
realize a lattice spin model with spin encoded in rotational states, prepared
and probed by microwaves. This spin-exchange interaction arises from the
resonant exchange of rotational angular momentum between two molecules. We
observe clear oscillations in the evolution of the spin coherence in addition
to an overall decay. The frequency of these oscillations, the strong dependence
of the spin coherence time on the lattice filling, and the effect of a
multi-pulse sequence designed to reverse dynamics due to two-body exchange
interactions all provide evidence of dipolar interactions. We also demonstrate
suppression of loss in weak lattices due to a quantum Zeno mechanism.
Measurements of these tunneling-induced losses allow us to independently
determine the lattice filling factor. These results comprise an initial
exploration of the behavior of many-body spin models with direct, long-range
spin interactions and lay the groundwork for future studies of many-body
dynamics in spin lattices.
