Optimal Cooling of Multiple Levitated Particles: Theory of Far-Field Wavefront-Shaping

TL;DR

This paper introduces a theoretical method using far-field wavefront shaping to simultaneously cool multiple levitated nano-particles, advancing the control of complex optomechanical systems.

Contribution

It proposes a novel approach based on the scattering matrix to optimize cooling of multiple particles, extending techniques beyond single-object systems.

Findings

The method can identify optimal wavefronts for efficient cooling.

Numerical simulations demonstrate robustness against environmental variations.

The approach is applicable to complex, multi-particle levitated systems.

Abstract

The opportunity to manipulate small-scale objects pushes us to the limits of our understanding of physics. Particularly promising in this regard is the interdisciplinary field of levitation, in which light fields can be harnessed to isolate nano-particles from their environment by levitating them optically. When cooled down towards their motional quantum ground state, levitated systems offer the tantalizing prospect of displaying mesoscopic quantum properties. Currently restricted to single objects with simple shapes, the interest in levitation is currently moving towards the manipulation of more complex structures, such as those featuring multiple particles or different degrees of freedom. Unfortunately, current cooling techniques are mostly designed for single objects and thus cannot easily be multiplexed to address such coupled many-body systems. Here, we present an approach based on the spatial modulation of light in the far-field to cool down multiple nano-objects in parallel. Our procedure is based on the experimentally measurable scattering matrix and on its changes with time. We demonstrate how to compose from these ingredients a linear energy-shift operator, whose eigenstates are identified as the incoming wavefronts that implement the most efficient cooling of complex moving ensembles of levitated particles. Submitted in parallel with arxiv:2103.12592, this article provides a theoretical and numerical study of the expected cooling performance as well as of the robustness of the method against environmental parameters.