  I demonstrate a simple example of how the time series obtained from searches
for ultralight bosonic dark matter (DM), such as the axion, can be used to
determine whether it is in a coherent or incoherent quantum state. The example
is essentially trivial, but I hope that explicitly addressing it provokes
experimental exploration. In the standard coherent state, $\mathcal{O}(1)$
oscillations in the number density occur over the coherence time, $\tau_c=h/m
v^2$, where $m$ is the particle mass and $v$ is the galactic virial velocity,
leading to a reduction in the constraining power of experiments operating on
timescales $T<\tau_c$, due to the unknown global phase. On the other hand if
the DM is incoherent then no such strong number oscillations occur, since the
ensemble average over particles in different streams gives an effective phase
average. If an experiment detects a signal then the coherent or incoherent
nature of DM can be determined by time series analysis over the coherence time.
This finding is observationally relevant for DM masses, $10^{-17}\text{
eV}\lesssim m\lesssim 10^{-11}\text{ eV}$ (corresponding to coherence times
between a year and 100 seconds), and can be explored by experiments including
CASPEr, DMRadio, and AION. Coherence may also be measurable at higher masses in
the microwave regime, but I have not explored it.
