Cooling the optical-spin driven limit cycle oscillations of a levitated gyroscope

Abstract

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.

Stroboscopic thermally-driven mechanical motion

“…Advantageously, experimental realisations of asymmetrical nonlinearities similar to kxy 2 , have been recently achieved in trapped ions 59,60 , SNAIL 61,62 and superconducting circuits 63 via trilinear interactions. Levitodynamics has already shown instances where such asymmetrical interactions can be in principle observed 41,57,64 , allowing for immediate experimental verification.…”

“…The possibilities recently demonstrated on the control of mechanical motion with nano-seconds sampling 19 , pave the way for testing this strategy in levitodynamics experiments. Alternatively, the asymmetric nonlinear potential can be fully engineered by non-conservative forces, where the back-action is completely removed leaving only the positive asymmetrical interaction to be exploited 57 .…”

Controlling Optomechanical Libration with the Degree of Polarization

“…A particularly enticing prospect is to harness levitated rotors as torque sensors [8], in applications ranging from photonic torque microscopy [11][12][13][14][15][16], to seismology [17,18] and space-based alignment procedures [19]. Another use case are tests of quantum coherence at macroscopic scales [20,21].…”

All-optical sub-Kelvin sympathetic cooling of a levitated microsphere in vacuum

“…While the lowest temperature of < ∼ 1 K agrees with the predictions in Figs. 1(b-d), nonconservative azimuthal forces can have significant effects on the dynamics of rotating levitated particles [15], and a more detailed model will be the subject of future work.…”