  We propose and analyze a scheme for sympathetic cooling of the translational
motion of polar molecules in an optical lattice, interacting one by one with
laser-cooled ions in a radio-frequency trap. The energy gap between the
excitation spectra of the particles in their respective trapping potentials is
bridged by means of a parametric resonance, provided by the additional
modulation of the RF field. We analyze two scenarios: simultaneous laser
cooling and energy exchange between the ion and the molecule, and a scheme when
these two processes take place separately. We calculate the lowest final energy
of the molecule and the cooling rate depending on the amplitude of the
parametric modulation. For small parametric modulation, the dynamics can be
solved analytically within the rotating wave approximation.
