Quantum Fluctuations of a Levitated Nanoparticle: An Analysis Within Nelson's Stochastic Mechanics Reformulation of Quantum Theory

ABSTRACT Levitodynamics, i.e., the levitation of objects of mesoscopic size has made huge progress in the last decade allowing to address some questions of fundamental physics for the first time. It has become possible to cool a levitated particle of mesoscopic size down to its motional ground state and to observe its motion driven by quantum fluctuations. This defines a quantum system that is ideally suited for an analysis within Nelson's stochastic mechanics approach to quantum mechanics, which allows for a dynamic description of individual particle paths. In good approximation, a levitated nanoparticle is a quantum harmonic oscillator. The coherent states of such an oscillator are superpositions of classical paths and the stochastic ground state process. They are exact solutions not only of the Schrödinger equation but also of the quantum Hamilton equations of Nelson's stochastic mechanics, and they are amenable to path simulations. All model parameters are typically available from experiment. Analyzing the quantum motion of the levitated nanoparticle in terms of the coherent states of a quantum harmonic oscillator allows for a quantitative prediction of the experimentally measured power spectral density of its position fluctuations and predicts new experimentally accessible measures for the mean number of phonons present in the center of mass motion. It also explains the observed phase space trajectory of the nano‐particle during cooling.