  Control of the external degree of freedom of trapped molecular ions is a
prerequisite for their promising applications to spectroscopy, precision
measurements of fundamental constants, and quantum information technology.
Here, we demonstrate near ground-state cooling of the axial motional modes of a
calcium mono-oxide ion via sympathetic sideband cooling with a co-trapped
calcium ion. We also show that the phonon state of the axial out-of-phase mode
of the ion chain is maintained while the mode frequency is adiabatically ramped
up and down. The adiabatic ramping of the motional mode frequency is a
prerequisite for searching for the proposed molecular dipole-phonon
interaction.
