We demonstrate time-of-flight measurements for an ultracold levitated
nanoparticle and reveal its translational velocity in the quantum regime. We
discover that the velocity distributions obtained with repeated measurements
are significantly broadened via librational motions of the nanoparticle. Under
feedback cooling on all the librational motions, we recover the velocity
distributions in reasonable agreement with an expectation from the occupation
number, with approximately twice the width of the quantum limit. The strong
impact of librational motions on the translational motions is understood as a
result of the deviation between the libration center and the center of mass,
induced by the asymmetry of the nanoparticle. Our results elucidate the
importance of the control over librational motions and establish the basis for
exploring quantum mechanical properties of levitated nanoparticles in terms of
their velocity.Comment: 7 pages, 7 file