  The equations of electrodynamics are altered in the presence of a classical
coherent axion dark matter background field, changing the dispersion relation
for electromagnetic waves. Careful measurements of the frequency stability in
sensitive atomic clocks could in principle provide evidence for such a
background for $f_a \ge 10^7$ GeV. Turning on a background magnetic field might
enhance these effects in a controllable way, and interferometric measurements
might also be useful for probing the time-varying photon dispersion relation
that results from a coherent cosmic axion background.
