  We show that the electric dipole-dipole interaction between a pair of polar
molecules undergoes an all-out transformation when superimposed by a far-off
resonant optical field. The combined interaction potential becomes tunable by
variation of wavelength, polarization and intensity of the optical field and
its dependence on the intermolecular separation exhibits a crossover from an
inverse-power to an oscillating behavior. The ability thereby offered to
control molecular interactions opens up avenues toward the creation and
manipulation of novel phases of ultracold polar gases among whose
characteristics is a long-range entanglement of the dipoles' mutual
orientation. We devised an accurate analytic model of such
optical-field-dressed dipole-dipole interaction potentials, which enables a
straightforward access to the optical-field parameters required for the design
of intermolecular interactions in the laboratory.
