  We show that the vibrations of an ion Coulomb crystal can be cooled to the
zero-point motion through the optomechanical coupling with a high-finesse
cavity. Cooling results from the interplay between coherent scattering of
cavity photons by the ions, which dynamically modifies the vibrational
spectrum, and cavity losses, that dissipate motional energy. The cooling
mechanism we propose requires that the length scales of the crystal and the
cavity are mismatched so that the system is intrinsically frustrated, leading
to the formation of defects (kinks). When the pump is strong enough, the
anti-Stokes sidebands of all vibrational modes can be simultaneously driven.
These dynamics can be used to prepare ultracold chains of dozens of ions within
tens of milliseconds in state-of-the-art experimental setups. In addition, we
identify parameter regimes of the optomechanical interactions where individual
localized modes can be selectively manipulated, and monitored through the light
at the cavity output. These dynamics exemplify robust quantum reservoir
engineering of strongly-correlated mesoscopic systems and could find
applications in optical cooling of solids.
