Quantum tomography of motion in time of flight

Quantum control of mechanical motion has been achieved in a surprising range of platforms in the past decades.  These mechanical quantum systems have both piqued the curiosity of physicists, and enabled new approaches to difficult tasks in manipulating quantum information.  Trapped particles offer one opportunity to study isolated quantum motion.  Laser-cooled ions routinely demonstrate intriguing phonon control, and recent experiments have now brought trapped dielectric nanoparticles to their quantum ground state.  In this talk I present how observing a particle after a time of flight combined with trap evolution can map the full quantum state of a trapped particle.  I will describe this intuitive method through experiments with a single neutral atom in a non-classical motional state, and discuss future applicability to larger mass systems.