Resolving gravitational redshift with sub-millimeter height differences using spin-squeezed optical clocks

The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential, also known as gravitational redshift, is one of the classical tests of Einstein’s theory of general relativity. Owing to their ultra-high accuracy and stability, state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference. Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing. Here, we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of ¹⁷¹Yb atoms. The numerical results illustrate that for a sample of 10⁴ atoms, the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm, corresponding to a fractional gravitational redshift at the 10⁻²⁰ level. In addition, the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms. Our work opens a door to the future spin-squeezing-enhanced test of general relativity.