  The spin in a rotating frame has attracted a lot of attentions recently, as
it deeply relates to both fundamental physics such as pseudo-magnetic field and
geometric phase, and applications such as gyroscopic sensors. However, previous
studies only focused on adiabatic limit, where the rotating frequency is much
smaller than the spin frequency. Here we propose to use a levitated
nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics
and the geometric phase of a rotating electron spin without adiabatic
approximation. We find that the transition between the spin levels appears when
the rotating frequency is comparable to the spin frequency at zero magnetic
field. Then we use Floquet theory to numerically solve the spin energy
spectrum, study the spin dynamics and calculate the geometric phase under a
finite magnetic field, where the rotating frequency to fulfill the resonant
transition condition could be greatly reduced.
