Time-of-flight velocity measurements for a levitated nanoparticle under the feedback control of its six degrees of freedom

Nanoparticles levitated in vacuum are expected to be a promising platform for various applications ranging from ultrasensitive accelerometers to investigations on macroscopic quantum physics and fundamental physics. In many applications, cooling the motions of nanoparticles is a crucial ingredient.

We demonstrate feedback cooling of all external degrees of freedom of an optically trapped neutral nanoparticle. Three center-of-mass motions are cooled near the ground state via optical cold damping. Because of the small deviations from a sphere, the nanoparticle exhibits three angular oscillations at three frequencies, which are understood via a simple model based on an anisotropic optical potential. The presence of an electric dipole moment in the nanoparticle enables us to cool all the angular oscillations via electric cold damping.

Furthermore, we realize the time-of-flight measurements for a feedback-controlled nanoparticle, where we obtain its velocity distribution by repeating a release-and-recapture protocol. The time-of-flight measurements have been expected as a means to realize quantum state tomography of a levitated nanoparticle. At high temperatures, the observed width of the velocity distribution agrees with the Maxwell-Boltzmann distribution. At low temperatures near the ground state, the width of the distribution is significantly broader than the expectation with the Maxwell-Boltzmann distribution. We elucidate that feedback cooling of three librational motions plays a crucial role to recover the expected narrow width. We establish a simple model to explain the broadening mechanism, where the asymmetry of the particle geometry couples librational motions and center-of-mass motions.