Multi-Particle Active Feedback Cooling Using Shaped Wave-Fronts

Abstract

Levitated particles offer a unique and controlled platform for precise investigations of various physical effects while minimizing external influences. The potential to perform high-precision force sensing experiments and explore quantum phenomena using cooled particles has emerged as an intriguing possibility. However, to fully unlock the complexity and capabilities of these systems, the simultaneous trapping and cooling of a large number of particles is crucial. This poses a challenge as existing techniques rely on controlled environments, making the scaling up to larger systems challenging due to intricate interactions between individual particles. Here, we propose a novel multi-particle cooling approach utilizing a generalization of the Wigner-Smith time-delay operator [1,2]. By establishing a connection between the eigenvalues of this operator and system changes, we leverage advancements in spatial light modulators to introduce an active feedback cooling scheme. Our scheme utilizes far-field information from the electromagnetic field to generate a sequence of customized input wave-fronts, which simultaneously cool the translational and rotational center-of-mass motion for all particles in parallel. Remarkably, our approach decouples the degrees of freedom of the field from those of the particles, naturally leading to good scaling properties. To validate the scalability of our approach, we conducted numerical simulations demonstrating its effectiveness across a wide range of particle numbers, sizes, and shapes. Based on these findings, we propose an experimental implementation wherein continuously shaped wave-fronts cool an ensemble of levitated objects, with the goal to observe and analyze the cooling effects in a practical setting using state of the art equipment.

References [1] J. Hüpfl, N. Bachelard, M. Kaczvinszki, M. Horodynski, M. Kühmayer, S. Rotter, Phys. Rev. Lett. 130, 083203(2023) [2] J. Hüpfl, N. Bachelard, M. Kaczvinszki, M. Horodynski, M. Kühmayer, S. Rotter, Phys. Rev. A. 107, 023112(2023)