Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control

Abstract

We use an optimal control protocol to cool one mode of the center-of-mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center-of-mass temperature of 5 mK at 3×10^−7mbar and transients 10–600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects. © 2019 American Physical Society.