Fig. 1: Experimental system and synchronous differential clock comparisons.

a A representative camera image of a spatially multiplexed array with five ensembles of ⁸⁷Sr atoms (indexed 1–5 from top to bottom) trapped in a vertical 1D optical lattice for differential clock comparisons. The spacing between neighboring ensembles is 0.25 cm, spanning a total height difference of 1 cm. Due to the gravitational redshift, clocks at a higher gravitational potential are predicted to tick faster than clocks at a lower potential. The gray box shows the orientations of the applied bias magnetic field (B), and the lattice and clock laser polarizations (ϵ). b A representative outcome from synchronous Ramsey spectroscopy on the \({\left.\right|}^{1}{S}_{0},\;{m}_{F}=+ 5/2\left.\right\rangle \leftrightarrow {\left.\right|}^{3}{P}_{0},\;{m}_{F}=+ 3/2\left.\right\rangle\) clock transition with a 10 s free precession time using five atomic ensembles, resulting in ten pairwise clock comparisons. In each plot, the excitation fractions of ensemble j are plotted against the excitation fractions of ensemble i (P_j: P_i, where j > i), tracing out an ellipse which is fitted to in order to extract the frequency difference between that pair. The frequency difference is dominated by the first-order differential Zeeman shift, which is rejected when averaging transitions between opposite spin states (Supplementary Note 3A).