Optimal control of levitated nanoparticles through finite-stiffness confinement

TL;DR

This paper develops a method to optimally control levitated nanoparticles using finite-stiffness confinement, accounting for inertial effects, and demonstrates experimental implementation with energy-efficient state transitions.

Contribution

It introduces a novel optimal control protocol for underdamped nanoparticles with bounded stiffness, combining theoretical derivation and experimental validation.

Findings

Achieved precise state transfer with minimal energy consumption.

Validated the protocol experimentally with optical levitation.

Reduced energy use compared to existing methods.

Abstract

Optimal control of levitated nanoparticles subjected to thermal fluctuations is a challenging problem, both theoretically and experimentally. In this Letter, we compute the time-dependent harmonic confining potential that steers, in a prescribed time and with the minimum energetic cost, a Brownian particle between two assigned equilibrium states. We take full account of inertial effects, thus addressing the general underdamped dynamics, and, to address actual experimental conditions, the stiffness of the confining potential is required to be bounded. We carry out an experiment realizing the described protocol for an optically confined nanoparticle, which is shown to reach the target state within accuracy -- while spending less energy than other protocols with the same duration, significantly shorter than the characteristic relaxation time. The results presented here are expected to have relevant applications in the design of optimal devices, such as engines at the nanoscale.