Einstein's theory of general relativity states that clocks at different gravitational potentials tick at different ratesan effect known as the gravitational redshift 1 . As fundamental probes of space and time, atomic clocks have long served to test this prediction at distance scales from 30 centimeters to thousands of kilometers 2-4 . Ultimately, clocks will study the union of general relativity and quantum mechanics once they become sensitive to the finite wavefunction of quantum objects oscillating in curved spacetime. Towards this regime, we measure a linear frequency gradient consistent with the gravitational redshift within a single millimeter scale sample of ultracold strontium. Our result is enabled by improving the fractional frequency measurement uncertainty by more than a factor of 10, now reaching 7.6×10 -21 . This heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations. Modern atomic clocks embody Arthur Schawlow's motto to "never measure anything but frequency." This deceptively simple principle, fueled by the innovative development of laser science and quantum technologies based on ultracold matter, has led to dramatic progress in clock performance. Recently, clock measurement precision reached the mid-19 th digit in one
Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a “magic” lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.
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