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

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 400μm and 2mm length, time dilation shifts of In{}^+ ions due to micromotion can be close to 1times10^-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.