Experimental demonstration of an efficient number diagnostic for long 1D ion chains

TL;DR

This paper experimentally validates a diagnostic method for accurately determining the number of ions in very long 1D ion chains by measuring ion distances and trap potential, achieving near 1% accuracy without counting.

Contribution

The study provides the first experimental validation of Dubin's model for long ion chains, enabling precise ion number diagnostics in quantum applications.

Findings

Achieved 4.5% uncertainty in ion number estimation

Measured ion distances with better than 2% precision

Validated Dubin's model for long ion chains

Abstract

Very long, one-dimensional (1D) ion chains are the basis for many applications, in particular in quantum information processing and reliable diagnostics are needed to quantify them. To that purpose, we have experimentally validated Dubin's model for very long ion chains [Phys. Rev. Lett. 71, 2753 (1993)]. This diagnostic allows to precisely determine the number of trapped ion with an accuracy of almost 1\% without counting them, by measuring the ion-ion distance of the innermost particles, as well as the trapping potential along the ion chain direction. In our experiment, based on a 155 ion chain, the central 30 ions are measured to be equidistant to better than 2\%, and we can determine the total number of trapped ions with a 4.5\% uncertainty, completely dominated by a conservative estimation of the experimental characterisation of the trap.