  Fundamental low-energy limits to the accuracy of quantum clock and stopwatch
models in which the clock hand motion is activated by the presence of a
particle in a region of space have been studied in the past, but their
relevance for actual atomic clocks had not been assessed. In this work we
address the effect of slow atomic quantum motion on Rabi and Ramsey resonance
fringe patterns, as a perturbation of the results based on classical atomic
motion. We find the dependence of the fractional error of the corresponding
atomic clocks on the atomic velocity and interaction parameters.
