Ground state cooling of weakly-coupled trapped-ion motion using parametric coupling*

Laser cooling of trapped-ion motional degrees of freedom to near their ground state is crucial for high-fidelity quantum information applications and high-precision quantum metrology. However certain motional degrees of freedom are weakly coupled to the available cooling light due to geometrical constraints or weak mode participation of the cooling ions. We overcome these obstacles by using parametric coupling to exchange motional energy between modes that are weakly and strongly coupled to the cooling light respectively. In this way we demonstrate cooling to near the ground state of some weakly coupled modes in Be+-Be+ and Be+-Mg+ two-ion crystals. In a Be+-Mg+-Be+ crystal, we cool all three axial modes to near the ground state using only the Mg+ ion, even though this ion does not participate in the stretch mode of this symmetric crystal.  This method may be useful for efficient cooling of Coulomb-crystals of many charged species, including molecular ions and highly charged ions.