  The non-conservative, azimuthal forces associated with inhomogeneous
optical-spin angular momentum play a critical role in optical trapping.
Intriguingly, birefringent microspheres can be stably levitated and rapidly
rotated in circularly polarized optical traps in ultra-high vacuum whereas
isotropic spheres are typically destabilized and expelled, even at relatively
modest pressures. Here we show that the resolution of this apparent key paradox
rests in the form of the orientationally averaged, effective forces acting on
the spinning birefringent particle. In particular, the effective azimuthal
component is heavily suppressed and highly non-linear. As a consequence,
non-conservative effects are strongly, if imperfectly, inhibited. Their
influence is apparent only at very low pressures where we observe the formation
of noisy, nano-scale limit cycles or orbits. Finally, we show how parametric
feedback can synthesize a form of dissipation, necessary to preserve limit
cycle oscillation, without introducing additional thermal fluctuations. This
allows the preparation of highly coherent, self-sustained oscillations with
effective temperatures on the order of a milliKelvin. The tailoring of
azimuthal spin forces through the material structure of a spinning,
non-spherical particle opens up new opportunities for the design of ultra
stable optical rotors. In addition, we have shown that the unique profile of
the azimuthal force, featured in this work, allows for the formation of
nano-scale limit cycles that can be stabilized and cooled. In principle, this
approach could enable the cooling of limit cycles into the quantum regime,
allowing for experimental realisation of quantum synchronization, or
alternative ways of entangling mesoscopic bodies.
