  Rotational excitation of polar molecules trapped in an optical lattice gives
rise to rotational excitons. Here we show that non-linear interactions of such
excitons can be controlled by an electric field. The exciton--exciton
interactions can be tuned to induce exciton pairing, leading to the formation
of biexcitons. Tunable non-linear interactions between excitons can be used for
many applications ranging from the controlled preparation of entangled
quasiparticles to the study of polaron interactions and the effects of
non-linear interactions on quantum energy transport in molecular aggregates.
