  Torque sensors such as the torsion balance enabled the first determination of
the gravitational constant by Cavendish and the discovery of Coulomb's law.
Torque sensors are also widely used in studying small-scale magnetism, the
Casimir effect, and other applications. Great effort has been made to improve
the torque detection sensitivity by nanofabrication and cryogenic cooling. The
most sensitive nanofabricated torque sensor has achieved a remarkable
sensitivity of $10^{-24} \rm{Nm}/\sqrt{\rm{Hz}}$ at millikelvin temperatures in
a dilution refrigerator. Here we dramatically improve the torque detection
sensitivity by developing an ultrasensitive torque sensor with an optically
levitated nanorotor in vacuum. We measure a torque as small as $(1.2 \pm 0.5)
\times 10^{-27} \rm{Nm}$ in 100 seconds at room temperature. Our system does
not require complex nanofabrication or cryogenic cooling. Moreover, we drive a
nanoparticle to rotate at a record high speed beyond 5 GHz (300 billion rpm).
Our calculations show that this system will be able to detect the long-sought
vacuum friction near a surface under realistic conditions. The optically
levitated nanorotor will also have applications in studying nanoscale magnetism
and quantum geometric phase.
