Evaluation of Doppler shifts to improve the accuracy of primary atomic fountain clocks

We demonstrate agreement between measurements and ab initio calculations of the frequency shifts caused by distributed cavity phase variations in the microwave cavity of a primary atomic fountain clock. Experimental verification of the finite element models of the cavities gives the first quantitative evaluation of this leading uncertainty and allows it to be reduced to δν/ν = ±8.4 × 10^-17. Applying these experimental techniques to clocks with improved microwave cavities will yield negligible distributed cavity phase uncertainties, less than ±1 × 10^-17.