Systematic uncertainty evaluation of an $^{27}$Al$^{+}$ quantum-logic clock

A previous optical atomic clock based on quantum-logic spectroscopy of the $^1S_0$ $\longleftrightarrow$ $^3P_0$ transition of $^{27}$Al$^{+}$ reached a systematic uncertainty of $\delta \nu / \nu = 8.0 \times 10^{-18}$ \footnote{C.-W. Chou,{\it et. al.}, PRL, \textbf{104}, 070802 (2010)},\footnote{C.-W. Chou, Private Communication}. This uncertainty was dominated by environmental effects related to the traps used to confine the ions; i.e. time-dilation shifts due to motion of the ions in the trap and the blackbody radiation (BBR) shift due to elevated trap temperature. Improvements in a new trap have reduced excess micromotion and secular heating, making it possible to operate the clock near the three-dimensional motional ground state \footnote{J.-S. Chen, {\it et. al.}, PRL, \textbf{118}, 053002, (2017)}, and leading to a reduced time-dilation shift uncertainty. In addition, the operating temperature of the system has been lowered to reduce the BBR shift uncertainty. Here we present the systematic uncertainty evaluation of a new $^{27}$Al$^{+}$ quantum-logic clock based on this improved trap design.