Observing and Verifying the Quantum Trajectory of a Mechanical Resonator.

Continuous weak measurement allows localizing open quantum systems in state space and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories of microwave photon and qubit states. We apply these concepts to a macroscopic mechanical resonator, and we follow the quantum trajectory of its motional state conditioned on a continuous optical measurement record. Starting with a thermal mixture, we eventually obtain coherent states of 78% purity-comparable to a displaced thermal state of occupation 0.14. We introduce a retrodictive measurement protocol to directly verify state purity along the trajectory, and we furthermore observe state collapse and decoherence. This opens the door to measurement-based creation of advanced quantum states, as well as potential tests of gravitational decoherence models.