Prospects of a thousand-ion Sn²⁺ Coulomb-crystal clock with sub-10^-19 inaccuracy.

Abstract

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn²⁺ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn²⁺ has a unique combination of features that is not available in previously considered ions: a ¹S₀ ↔  ³P₀ 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 Sn²⁺ Coulomb-crystal clocks.