Optimal control for feedback cooling in cavityless levitated optomechanics

Luca Ferialdi,Ashley Setter,Marko Toroš,Chris Timberlake,Hendrik Ulbricht

doi:10.1088/1367-2630/ab2b69

Abstract

We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a state estimation scheme that takes into account the modulation of the laser intensity. We show that such an implementation allows us to increase the feedback strength, leading to faster cooling rates and lower center-of-mass temperatures.

Highlights

The ability to precisely control and cool the motion of mechanical resonators in order to generate quantum states is of great interest for testing fundamental physics, such as investigating the quantum-to-classical transition [1, 2]
We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the licence
In order for any of these resonator systems to approach the quantum regime, their motion must first be cooled to close to the ground state, which can be achieved with cryogenically cooling the environment or with active feedback schemes

Summary

Introduction

The ability to precisely control and cool the motion of mechanical resonators in order to generate quantum states is of great interest for testing fundamental physics, such as investigating the quantum-to-classical transition [1, 2]. Optically levitated silica particles have had their centerof-mass motion cooled to millikelvin [11,12,13,14] and sub-millikelvin [15, 16] temperatures, whereas nanodiamonds [17, 18] have been used for spin coupling experiments [19, 20] Other levitation mechanisms, such as Paul traps [21], hybrid electro-optical traps [22], and magnetic traps [23,24,25] have been proposed as candidates for preparing macroscopic quantum states [26,27,28] and testing spontaneous collapse models [29, 30]. In order for any of these resonator systems to approach the quantum regime, their motion must first be cooled to close to the ground state, which can be achieved with cryogenically cooling the environment or with active feedback schemes

Objectives

Discussion

Conclusion