Bayesian Estimation of Experimental Parameters in Stochastic Inertial Systems: Theory, Simulations, and Experiments with Objects Levitated in Vacuum

0574797 - ÚPT 2024 RIV US eng J - Journal Article
Šiler, Martin - Svak, Vojtěch - Jonáš, Alexandr - Simpson, Stephen Hugh - Brzobohatý, Oto - Zemánek, Pavel
Bayesian Estimation of Experimental Parameters in Stochastic Inertial Systems: Theory, Simulations, and Experiments with Objects Levitated in Vacuum.
Physical Review Applied. Roč. 19, č. 6 (2023), č. článku 064059. ISSN 2331-7019. E-ISSN 2331-7019
R&D Projects: GA ČR(CZ) GF21-19245K; GA MŠMT(CZ) EF16_026/0008460
Grant - others:AV ČR(CZ) AP2002
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:68081731
Keywords : optical levitation * force estimation * stochastic processes
OECD category: Optics (including laser optics and quantum optics)
Impact factor: 4.6, year: 2022
Method of publishing: Open access
https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.064059 https://arxiv.org/pdf/2212.14043

High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experi-ments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the interplay between acting external forces, viscous dissipation, and random driving by the thermal environment. The relevance of inertia then dictates that both position and momentum must, in principle, be known to fully describe the system, which makes its quantitative exper-imental characterization rather challenging. We introduce a general method of Bayesian inference of the force field and environmental parameters in stochastic inertial systems that operates solely on the time series of recorded noisy positions of the system. The method is first validated on simulated trajectories of model stochastic harmonic and anharmonic oscillators with damping. Subsequently, the method is applied to experimental trajectories of particles levitating in tailored optical fields and used to characterize the dynamics of particle motion in a nonlinear Duffing potential, a static or time-dependent double-well poten-tial, and a nonconservative force field. The presented inference procedure does not make any simplifying assumptions about the nature or symmetry of the acting force field and provides robust results with tra-jectories 2 orders of magnitude shorter than those typically required by alternative inference schemes. In addition to being a powerful tool for quantitative data analysis, it can also guide experimentalists in choosing appropriate sampling frequency (at least 20 measured points per single characteristic period) and length of the measured trajectories (at least 10 periods) to estimate the force field and environmental characteristics with a desired accuracy and precision.
Permanent Link: https://hdl.handle.net/11104/0344833