  An optically levitated nanoparticle in vacuum is a paradigm optomechanical
system for sensing and studying macroscopic quantum mechanics. While its
center-of-mass motion has been investigated intensively, its torsional
vibration has only been studied theoretically in limited cases. Here we report
the first experimental observation of the torsional vibration of an optically
levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the
coupling between the spin angular momentum of photons and the torsional
vibration of a nonspherical nanoparticle whose polarizability is a tensor. The
torsional vibration frequency can be one order of magnitude higher than its
center-of-mass motion frequency, which is promising for ground state cooling.
We propose a simple yet novel scheme to achieve ground state cooling of its
torsional vibration with a linearly-polarized Gaussian cavity mode. A levitated
nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale
torsion balance with a torque detection sensitivity on the order of $10^{-29}
~\mathrm{N}\cdot \mathrm{m}/\sqrt{\mathrm{ Hz}}$ under realistic conditions.
