Ion-assisted ground-state cooling of a trapped polar molecule

We propose and analyze a scheme for sympathetic cooling of the translational motion of polar molecules confined in the wells of a deep optical lattice and 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 where 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.