Stochastic Non-linear Dynamics of Optically Trapped Particles

Luca ORNIGOTTI

Doctoral thesis

Stochastic nonlinear dynamics of optically trapped

Abstract:

The fast pace that optically levitated platforms have experienced over the past decade has opened new ways to investigate a plethora of nonlinear stochastic mechanical effects. Amongst them, noise-to-signal transitions, peculiar and interesting processes in physics, are the focus of this thesis. They allow to transform the environmental noise to useful mechanical effects. This thesis investigates the paradigm of stochastic highly nonlinear dynamics of a levitated nanosphere in the classical, overdamped and underdamped regime. With main focus on the dynamical noise-to-signal transitions in the optical cubic potential V (x) = kx3/3, where its inherent instabilities were positively exploited as a thermally driven source to autonomously transform noise into useful coherent mechanical displacement. Such transformation can be performed because the nonlinearity, one of the essential ingredients together with instabilities, brings the mechanical system out of its thermal equilibrium, thus allowing energy from the fluctuating environment to be used as a source of coherent mechanical displacement and oscillations. The first part of the thesis opens with a general overview of stochastic processes in linear oscillators, stable and unstable, in the high and low friction regime. General nomenclature and analytical methods are introduced. The second part discusses stability and noise-to-signal transitions for a particle in cubic potential in the overdamped regime followed by the investigation of maximum of position distribution as a new methodology to characterise the dynamics of highly non-linear systems. Moreover, the underdamped dynamics of a particle in cubic potential is discussed, introducing new unexplored nonlinear ballistic effects appearing in the instantaneous speed and acceleration, obtained for parameters of current underdamped experiments. Last, but not least, the numerical methodology to compute dynamics in highly unstable systems, subjected to rapid diverging trajectories, is discussed; with focus on accuracy of computation within and beyond the characteristic time of divergence.

Abstract:

The fast pace that optically levitated platforms have experienced over the past decade has opened new ways to investigate a plethora of nonlinear stochastic mechanical effects. Amongst them, noise-to-signal transitions, peculiar and interesting processes in physics, are the focus of this thesis. They allow to transform the environmental noise to useful mechanical effects. This thesis investigates the paradigm of stochastic highly nonlinear dynamics of a levitated nanosphere in the classical, overdamped and underdamped regime. With main focus on the dynamical noise-to-signal transitions in the optical cubic potential V (x) = kx3/3, where its inherent instabilities were positively exploited as a thermally driven source to autonomously transform noise into useful coherent mechanical displacement. Such transformation can be performed because the nonlinearity, one of the essential ingredients together with instabilities, brings the mechanical system out of its thermal equilibrium, thus allowing energy from the fluctuating environment to be used as a source of coherent mechanical displacement and oscillations. The first part of the thesis opens with a general overview of stochastic processes in linear oscillators, stable and unstable, in the high and low friction regime. General nomenclature and analytical methods are introduced. The second part discusses stability and noise-to-signal transitions for a particle in cubic potential in the overdamped regime followed by the investigation of maximum of position distribution as a new methodology to characterise the dynamics of highly non-linear systems. Moreover, the underdamped dynamics of a particle in cubic potential is discussed, introducing new unexplored nonlinear ballistic effects appearing in the instantaneous speed and acceleration, obtained for parameters of current underdamped experiments. Last, but not least, the numerical methodology to compute dynamics in highly unstable systems, subjected to rapid diverging trajectories, is discussed; with focus on accuracy of computation within and beyond the characteristic time of divergence.

Keywords

Nonlinear Dynamics, Optical Trapping and Manipulation, Brownian Motion, Transient Stochastic Effects, Non-equilibrium Statistical Mechanics

Language used: English

Date on which the thesis was submitted / produced: 18. 6. 2021

Thesis defence

• Supervisor: prof. Mgr. Radim Filip, Ph.D.

Palacký University Olomouc

Faculty of Science

Doctoral programme / field:
Physics / Optics and Optoelectronics