Sympathetic cooling of molecular ion motion to the ground state

We demonstrate sympathetic sideband cooling of a \(^{40}\)CaH\(^{+}\) molecular ion co-trapped with a \(^{40}\)Ca\(^{+}\) atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion \(\overline{n}_{\mathrm{COM}} = 0.13 \pm 0.03\), corresponding to a temperature of \(12.47 \pm 0.03 ~\mu\)K. The breathing mode is cooled to \(\overline{n}_{\mathrm{BM}} = 0.05 \pm 0.02\), corresponding to a temperature of \(15.36 \pm 0.01~\mu\)K.