  We report an experimental observation of a record-breaking ultra-high
rotation frequency about 6 GHz in an optically levitated nanoparticle system.
We optically trap a nanoparticle in the gravity direction with a high numerical
aperture (NA) objective lens, which shows significant advantages in
compensating the influences of the scattering force and the photophoretic force
on the trap, especially at intermediate pressure (about 100 Pa). This allows us
to trap a nanoparticle from atmospheric to low pressure ($10^{-3}$ Pa) without
using feedback cooling. We measure a highest rotation frequency about 4.3 GHz
of the trapped nanoparticle without feedback cooling and a 6 GHz rotation with
feedback cooling, which is the fastest mechanical rotation ever reported to
date. Our work provides useful guides for efficiently observing hyperfast
rotation in the optical levitation system, and may find various applications
such as in ultrasensitive torque detection, probing vacuum friction, and
testing unconventional decoherence theories.
