  Levitation optomechanics exploits the unique mechanical properties of trapped
nano-objects in vacuum in order to address some of the limitations of clamped
nanomechanical resonators. In particular, its performance is foreseen to
contribute to a better understanding of quantum decoherence at the mesoscopic
scale as well as to lead to novel ultra-sensitive sensing schemes. While most
efforts have so far focused on optical trapping of low absorbing silica
particles, further opportunities arise from levitating objects with internal
degrees of freedom like color centers. Nevertheless, inefficient heat
dissipation at low pressures poses a challenge, as most nano-objects, even with
low absorbing materials, experience photo-damage in an optical trap. Here, by
using a Paul trap, we demonstrate levitation in vacuum and center-of-mass
feedback cooling of a nanodiamond hosting a single nitrogen-vacancy center. The
achieved level of motion control enables us to optically interrogate and
characterize the emitter response. The developed platform is applicable to a
wide range of other nano-objects and represents a promising step towards
coupling internal and external degrees of freedom.
