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

Abstract

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\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}21}$ 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.