Resolving the gravitational redshift within a millimeter atomic sample

TL;DR

This paper demonstrates the measurement of gravitational redshift within a millimeter-scale atomic sample, achieving unprecedented precision and highlighting the need for intra-sample gravitational corrections in future quantum clock experiments.

Contribution

The study reports the first measurement of gravitational redshift at millimeter scales using ultracold strontium atoms with over tenfold improved precision.

Findings

Measured a linear frequency gradient consistent with gravitational redshift at millimeter scale

Achieved fractional frequency measurement uncertainty of 7.6×10⁻²¹

Highlights the importance of intra-sample gravitational corrections for future quantum clocks

Abstract

Einstein's theory of general relativity states that clocks at different gravitational potentials tick at different rates - an effect known as the gravitational redshift. 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. 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$\times 10^{-21}$. This heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations.