A $^{87}$Sr Optical Lattice Clock

We report on our recent progress on a optical atomic clock with high accuracy and stability based on ultracold fermionic lattice-confined $^{87}$Sr atoms. We have evaluated the systematic effects at $1\times 10^{-16}$, enabling an improved measurement of the absolute clock transition frequency. The frequency of the $^1S_0$-$^3P_0$ transition was measured as $429\,228\,004\,229\,873.83 \pm 0.37$~Hz, where the final fractional uncertainty represents one of the most accurate measurements of an optical atomic frequency to date. In combination with data from the Paris and Tokyo groups, this measurement is used to limit Local Position Invariance by limiting coupling of fundamental constants to the gravitational potential.