Prospects of a thousand-ion Sn$^{2+}$ Coulomb-crystal clock with sub-$10^{-19}$ inaccuracy

TL;DR

This paper proposes a highly precise optical atomic clock using a large Coulomb crystal of Sn$^{2+}$ ions, leveraging unique atomic features to achieve sub-$10^{-19}$ accuracy, with potential for practical implementation.

Contribution

It introduces a novel many-ion optical clock based on Sn$^{2+}$ ions with unique properties for immunity to perturbations and discusses its potential accuracy and feasibility.

Findings

Estimated accuracy below 10^{-19}

Identified atomic properties enabling shift cancellation

Demonstrated feasibility of large Coulomb crystal clocks

Abstract

We propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn$^{2+}$ ions confined in a linear RF Paul trap. Sn$^{2+}$ has a unique combination of features that is not available in previously considered ions: a $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn$^{2+}$ Coulomb-crystal clocks.