Laser-cooled ¹⁷¹<i>Yb</i>⁺ microwave clock with a systematic uncertainty of 7.8×10⁻¹⁵

We present a transportable laser-cooled ion microwave clock based on the ground-state hyperfine splitting of ¹⁷¹<i>Yb</i>⁺. The system achieves a systematic uncertainty of 7.8×10^-15 and a short-term frequency stability of 9.5×10^-13/<i>τ</i>. Enhancements to the magnetic-field system suppress the decoherence process in the multi-body ion ensemble and reduce the second-order Zeeman frequency shift by a factor of two. The absolute microwave frequency is measured to be 12 642 812 118.468 6(3) Hz, consistent with the previous measurements and demonstrating twice the precision of the current state-of-the-art.