  The linear momentum and angular momentum of virtual photons of quantum vacuum
fluctuations can induce the Casimir force and the Casimir torque, respectively.
While the Casimir force has been measured extensively, the Casimir torque has
not been observed experimentally though it was predicted over forty years ago.
Here we propose to detect the Casimir torque with an optically levitated
nanorod near a birefringent plate in vacuum. The axis of the nanorod tends to
align with the polarization direction of the linearly polarized optical
tweezer. When its axis is not parallel or perpendicular to the optical axis of
the birefringent crystal, it will experience a Casimir torque that shifts its
orientation slightly. We calculate the Casimir torque and Casimir force acting
on a levitated nanorod near a birefringent crystal. We also investigate the
effects of thermal noise and photon recoils on the torque and force detection.
We prove that a levitated nanorod in vacuum will be capable of detecting the
Casimir torque under realistic conditions.
