Resolving the gravitational redshift across a millimetre-scale atomic sample

Einstein’s theory of general relativity states that clocks at different gravitational potentials tick at different rates relative to lab coordinates—an 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 centimetres to thousands of kilometres 2 – 4 . Ultimately, clocks will enable the study of the union of general relativity and quantum mechanics once they become sensitive to the finite wavefunction of quantum objects oscillating in curved space-time. Towards this regime, we measure a linear frequency gradient consistent with the gravitational redshift within a single millimetre-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. Reducing the fractional uncertainty over the measurement of the frequency of an ensemble of trapped strontium atoms enables observation of the gravitational redshift at the submillimetre scale.