Simultaneous ground-state cooling of six mechanical modes of two levitated nanoparticles

TL;DR

This paper demonstrates the simultaneous ground-state cooling of six mechanical modes in two levitated nanoparticles by controlling polarization angles in a coupled cavity system, advancing macroscopic quantum research.

Contribution

It introduces a polarization-angle-controlled coupled cavity system enabling simultaneous ground-state cooling of multiple nanoparticle modes, a novel approach in quantum manipulation.

Findings

Successful derivation of a seven-mode Hamiltonian for the system.

Identification of dark modes that hinder cooling and how to suppress them.

Effective control of coupling channels through polarization tuning.

Abstract

Ground-state cooling is a prerequisite for exploring macroscopic quantum effects in mechanical motion of massive objects. Here we construct a polarization-angle-controllable coupled cavity-levitated-nanoparticle system in which two nanoparticles trapped by individual tweezers are coupled to a single-mode field in a cavity. We also study the simultaneous ground-state cooling of six mechanical displacement modes of the two levitated nanoparticles through the coherent scattering mechanism. By deriving the Hamiltonian of the system and performing the linearization, we obtain a linearized seven-mode Hamiltonian, which can exhibit the coupling structure and cooling mechanism. We confirm the physical condition for the appearance of dark modes, which will suppress the simultaneous ground-state cooling of these mechanical modes. We also find that, by properly tuning the polarization angle $\theta $ between the cavity field and the optical tweezer fields, the coupling channels can be controlled on demand and simultaneous ground-state cooling of these six motional modes of the two nanoparticles can be realized. Our work paves the way for generation and manipulation of collective macroscopic quantum effects in multiple levitated nanoparticles.