Optimal cooling of multiple levitated particles: Theory of far-field wavefront shaping

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 nanoparticles from their environment by levitating them optically. When cooled towards their motional quantum ground state, levitated systems offer the tantalizing prospect of displaying mesoscopic quantum properties. While the interest in levitation has so far been focused mainly on manipulating individual objects with simple shapes, the field is currently moving towards the control 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 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 Hupfl et al. [Phys. Rev. Lett. 130, 083203 (2023)], 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.

Automated summary

The opportunity to manipulate small-scale objects pushes our understanding of physics to its limits. Levitation, an interdisciplinary field utilizing light fields to optically levitate nanoparticles, holds great promise in this regard. By cooling levitated systems towards their quantum ground state, mesoscopic quantum properties can potentially be observed. While the focus of levitation has mainly been on manipulating individual objects with simple shapes, the field is now moving towards the control of more complex structures. However, current cooling techniques are not readily applicable to coupled many-body systems, requiring new approaches. This article presents a method based on light modulation in the far field to cool multiple nano-objects simultaneously, providing a theoretical and numerical study of the cooling performance and method's robustness against environmental parameters.