Acoustic and Optical Properties of a Fast Spinning Dielectric Nanoparticle.

Nanoparticles levitated in vacuum can be set to spin at ultimate frequencies, limited only by the tensile strength of the material. At such high frequencies, drastic changes to the dynamics of solid-state quantum excitations are to be expected. Here, we theoretically describe the interaction between acoustic phonons and the rotation of a nanoparticle around its own axis, and model how the acoustic and optical properties of the nanoparticle change when it rotates at a fixed frequency. As an example, we analytically predict the scaling of the shape, the acoustic eigenmode spectrum, the permittivity, and the polarizability of a spinning dielectric nanosphere. We find that the changes to these properties at frequencies of a few GHz achieved in current experiments should be measurable with presents technology. Our work is a first step towards exploring solid-state quantum excitations in mesoscopic matter under extreme rotation, a regime that is now becoming accessible with the advent of precision control over highly isolated levitated nanoparticles.