  We show how the interference between spatially separated states of the center
of mass (COM) of a mesoscopic harmonic oscillator can be evidenced by coupling
it to a spin and performing solely spin manipulations and measurements (Ramsey
Interferometry). We propose to use an optically levitated diamond bead
containing an NV center spin. The nano-scale size of the bead makes the
motional decoherence due to levitation negligible. The form of the spin-motion
coupling ensures that the scheme works for thermal states so that moderate
feedback cooling suffices. No separate control or observation of the COM state
is required and thereby one dispenses with cavities, spatially resolved
detection and low mass-dispersion ensembles. The controllable relative phase in
the Ramsey interferometry stems from a gravitational potential difference so
that it uniquely evidences coherence between states which involve the whole
nano-crystal being in spatially distinct locations.
