Dmitry S. Bykov

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.

Radiofrequency (RF) traps enable highly controlled interactions between charged particles, including reactions between cold molecular ions, sympathetic cooling of one ion species with another, and quantum logic spectroscopy. However, the charge-to-mass ($Q/m$) selectivity of RF traps limits the range of objects that can be confined simultaneously in the same trap. Here, we confine two particles - a nanoparticle and an atomic ion - in the same radiofrequency trap although their charge-to-mass ratios differ by six orders of magnitude. The confinement is enabled by a dual-frequency voltage applied to the trap electrodes. We introduce a robust loading procedure under ultra-high vacuum and characterize the stability of both particles. It is observed that slow-field micromotion, an effect specific to the dual-field setting, plays a crucial role for ion localization. Our results lay the groundwork for controlled interactions between diverse charged particles, regardless of the difference in their charge or mass, with applications from antimatter synthesis to the generation of macroscopic quantum states of motion.