Evaluation of the systematic shifts of a ${}^{40}\textrm{Ca}^+-{}^{27}\textrm{Al}^+$ optical clock

TL;DR

This paper evaluates the systematic shifts and uncertainty of a ${}^{27} extrm{Al}^+$ optical clock sympathetically cooled by ${}^{40} extrm{Ca}^+$, achieving a total uncertainty of 7.9×10⁻¹⁸ and measuring frequency stability.

Contribution

It provides the first detailed assessment of systematic shifts and uncertainty for a ${}^{27} extrm{Al}^+$ clock cooled by ${}^{40} extrm{Ca}^+$, highlighting the dominant Zeeman shift uncertainty.

Findings

Total systematic uncertainty: 7.9×10⁻¹⁸

Frequency stability: 3.7×10⁻¹⁴/√τ

Main limitation: quadratic Zeeman shift

Abstract

Quantum-logic-based ${}^{27}\textrm{Al}^+$ optical clock has been demonstrated in several schemes as there are different choices of the auxiliary ion species. In this paper, we present the first detailed evaluation of the systematic shift and the total uncertainty of an ${}^{27}\textrm{Al}^+$ optical clock sympathetically cooled by a ${}^{40}\textrm{Ca}^+$ ion. The total systematic uncertainty of the ${}^{40}\textrm{Ca}^+ - {}^{27}\textrm{Al}^+$ quantum logic clock has been estimated to be $7.9 \times 10^{-18}$, which was mainly limited by the uncertainty of the quadratic Zeeman shift. By comparing the frequency of two counter-propagating clock beams on the same ion, we measured the frequency stability to be $3.7 \times 10^{-14} /\sqrt{\tau}$.