New Limits on Coupling of Fundamental Constants to Gravity by Absolute Frequeny Measurements of $^{87}$Sr Optical Lattice Clocks

We have measured the $^{87}$Sr ${{^1}\mathrm{S}_0}$-${{^3}\mathrm{P}_0}$ clock transition at $\nu_{\mathrm{Sr}} = 429\,228\,004\,229\,873.83\pm 0.37$~Hz, limited by statistical uncertainty of the Sr/Cs comparison. Three international laboratories agree on the absolute frequency at the $1\times 10^{-15}$ (Boulder, Paris) to $4\times 10^{-15}$ (Boulder, Paris, Tokyo) level, making $\nu_{\mathrm{Sr}}$ the best agreed-upon optical frequency to date. We analyze the global Sr frequency record to test Local Position Invariance by obtaining the best limits to date on coupling of fundamental constants to the ambient gravitational potential.