Probing Time Dilation in Coulomb Crystals in a high-precision Ion Trap

TL;DR

This paper introduces a scalable platform for high-precision spectroscopy of Coulomb ion crystals, demonstrating control over micromotion-induced time dilation shifts, advancing the development of entanglement-enhanced ion clocks.

Contribution

The work presents a new technique for measuring and minimizing micromotion in large ion crystals, enabling systematic shifts below 10^{-19} and improving clock stability.

Findings

Achieved sub-nanometer amplitude uncertainties in micromotion measurements.

Demonstrated time dilation shifts near 10^{-19} in large ion crystals.

Enabled systematic control of micromotion for many-ion quantum systems.

Abstract

Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of $10^{-18}$ and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, scalable platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as $10^{-19}$. Using a newly developed technique, we observe 3D excess micromotion amplitudes inside a Coulomb crystal with atomic spatial resolution and sub-nanometer amplitude uncertainties. We show that in ion Coulomb crystals of 400$\mu$m and 2mm length, time dilation shifts of In${}^+$ ions due to micromotion can be close to $1\times10^{-19}$ and below $10^{-18}$, respectively. In previous ion traps, excess micromotion would have dominated the uncertainty budget for spectroscopy of even a few ions. By minimizing its contribution and providing a means to quantify it, this work opens up the path to precision spectroscopy in many-body ion systems, enabling entanglement-enhanced ion clocks and providing a well-controlled, strongly coupled quantum system.