Differential Stark shifts in the hydrogen maser

The theory of the Stark shift of hydrogen ground-state hyperfine levels has been tested at the 2.4% level of accuracy in a hydrogen maser. The quadratic-Stark-shift coefficient for the hyperfine-transition frequency was experimentally found to be $\left|\delta \nu \mathrm{}\right|=8.448\left(206\mathrm{}\right)\mathrm{}\times {10}^{-14\mathrm{}}$ Hz ${\mathrm{}(\mathrm{V}/\mathrm{m})\mathrm{}}^{-2\mathrm{}}$, where the electric field was perpendicular to the axis of quantization. The quoted uncertainty corresponds to one standard deviation. The uncertainty has contributions from the statistics of the data and from systematic effects. A number of possible sources of systematic error or unwanted frequency shifts has been tested. The theoretically predicted coefficient $\left|\delta \nu \right|=8.236\mathrm{}\times {10}^{-14\mathrm{}}$ Hz ${\mathrm{}(\mathrm{V}/\mathrm{m})\mathrm{}}^{-2\mathrm{}}$ is in reasonable agreement with the present experimental result.