Quantum theory of electrically levitated nanoparticle-ion systems: Motional dynamics and sympathetic cooling

TL;DR

This paper develops a quantum theoretical framework for the coupled motional dynamics of a nanoparticle and ions in a trap, demonstrating sympathetic cooling to sub-kelvin temperatures and scalable cooling rates.

Contribution

It introduces a comprehensive quantum model for nanoparticle-ion systems, enabling analysis of motional cooling and non-Gaussian state preparation in levitated nanoparticles.

Findings

Motional frequencies and trajectories derived analytically.

Sympathetic cooling to sub-kelvin temperatures predicted.

Cooling rate increases linearly with the number of ions.

Abstract

We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of $N$ ions, predicting a linear increase of the cooling rate as a function of $N$ and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.