Measuring the Gravitational Redshift at the Centimeter-Scale using a Multiplexed Optical Lattice Clock

Precision tests of general relativity allow for searches of beyond standard model physics at new energy and length scales. In addition, measurements of general relativistic time-dilation with optical atomic clocks have been proposed as a new tool for mapping Earth's gravitational potential with sub-centimeter height resolution. We report progress towards testing the gravitational redshift predicted by general relativity at the centimeter and sub-centimeter scale. We perform synchronous differential measurements between multiple ensembles of ultra-cold neutral ⁸⁷Sr separated by a centimeter or less in height within a 1D optical lattice. We recently demonstrated a relative fractional frequency uncertainty between two ensembles of 8.9x10^-20 in this system, corresponding to a statistical uncertainty of a part in ten of the expected redshift at 1 cm [1]. We present a differential systematics budget summarizing our ongoing evaluation of the differential perturbations to these ensembles at the requisite levels of systematic uncertainty. Finally, we present planned upgrades to improve our multiplexed clock's stability and accuracy.

[1] X. Zheng et al., Differential clock comparisons with a multiplexed optical lattice clock, Nature in press (2022), preprint available at arXiv:2109.12237