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

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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 temperature of $50\pm22 \mu$K, achieved by minimizing the technical pointing noise of the trapping laser.

• This low noise leads to an acceleration and force sensitivity of $95\pm41$ 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 force sensitivity is comparable to that demonstrated for optically levitated nanospheres that are $10^4$ times less massive, corresponding to an acceleration sensitivity that is several orders of magnitude better.
• It is further shown that under these conditions the spheres remain stably trapped at pressures of $\sim 10^{-7}$ mbar with no active cooling for periods longer than a day.