Search for a coupling of the Earth’s gravitational field to nuclear spins in atomic mercury

We have measured the ratio of nuclear spin-precession frequencies of ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ and ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$ atoms for two orientations of magnetic field relative to the Earth’s gravitational field. We find that the spin-dependent component of gravitational energy is less than 2.2×${10}^{\mathrm{-}21}$ eV, a substantial improvement over previous limits. Our result provides a test of the equivalence principle for nuclear spins, and sets limits on the magnitude of possible scalar-pseudoscalar interactions which would couple to the spins.