Unraveling underlying order from its noisy fingerprints

High-quality mechanical oscillators can sensitively probe force, mass, or displacement in experiments extending from cosmologic scales down to the quantum realm. Stochastic trajectories of such dynamical systems in contact with a heat bath then uniquely report on both deterministic forces and random thermal noise that drive them. We developed a procedure for inferring the local forces , ambient temperature, and friction solely from the recorded traces of system’s positions, without the need to approximate the unmeasurable velocity. Our procedure based on Bayesian inference can be applied to a general inertial system subjected to an external force field containing conservative, non-conservative, or time-varying components, including systems out of thermal equilibrium for which conventional methods of inference fail or do not exist. The system parameters can be reliably rendered from very short trajectories, which is particularly important for characterizing transient phenomena. Unlike the previously reported strategies, our method explicitly deals with parameter estimation in the presence of the detection noise. Systematic analysis of experimental trajectories of micro and nano particles levitated in tailored optical fields revealed the utility of our method in quantitative optomechanical experiments that represent a unique platform for studying fundamental theoretical concepts of quantum physics on a macroscopic scale.

See Phys. Rev. Applied 19, 064059  https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.064059