We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching $5\times {10}^{-17}$ after a 1 h integration time. We put the first experimental upper bound on the multipolar $M1$ and $E2$ interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the ${10}^{-17}$ level, even for lattices as deep as 150 recoil energies.

• Received 3 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.210801