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This paper demonstrates cooling of the center-of-mass motion of 10$\mu$m-diameter optically levitated silica spheres to an effective temperatureof $50\pm22 \mu$K, achieved by minimizing the technical pointing noise of thetrapping laser. This low noise leads to an acceleration and force sensitivityof $95\pm41$ n$g/\sqrt{\mathrm{Hz}}$ ($g = 9.8$ m/s$^2$) and $0.95\pm0.11$aN$/\sqrt{\mathrm{Hz}}$, respectively, at frequencies near 50 Hz. This forcesensitivity is comparable to that demonstrated for optically levitatednanospheres that are $10^4$ times less massive, corresponding to anacceleration sensitivity that is several orders of magnitude better. It isfurther shown that under these conditions the spheres remain stably trapped atpressures of $\sim 10^{-7}$ mbar with no active cooling for periods longer thana day. Feedback cooling is still necessary in the moderate-pressure regime,motivating a comprehensive study of the loss mechanisms of the microspheres andproviding better understanding of the requirements for feedback-free opticaltrapping in vacuum. This work can enable high-sensitivity searches foraccelerations and forces acting on micron-sized masses, including those thatcould be produced by new physics beyond the Standard Model.

Force and acceleration sensing with optically levitated nanogram masses at microkelvin temperatures