Measuring atom positions in a microwave cavity to evaluate distributed cavity phase shifts

Distributed cavity phase (DCP) frequency shifts are a leading systematic effect in atomic fountain frequency standards. They originate from the phase variations of the field in the microwave cavity combined with different positions of the atoms in the cavity on the ascent and descent. Here we demonstrate techniques to precisely determine the position of the cloud of atoms in the microwave cavity, using either the approximately linear variation of the transverse components of the microwave field or the quadratic variation of the longitudinal microwave field amplitude in the cavity. We also show that shifting the initial position of the atoms gives a significantly higher sensitivity to DCP variations than the often-used tilting of fountains. A demonstrated centring precision of order 50 micrometres will enable DCP frequency shift uncertainties to be reduced to less than 10^-17 and thereby contribute insignificantly to the accuracy budget of a standard. These techniques to vertically align a fountain are straightforward to automate for routine operation and require a negligible fraction of the standard's averaging time.