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I demonstrate a simple example of how the time series obtained from searchesfor ultralight bosonic dark matter (DM), such as the axion, can be used todetermine whether it is in a coherent or incoherent quantum state. The exampleis essentially trivial, but I hope that explicitly addressing it provokesexperimental exploration. In the standard coherent state, $\mathcal{O}(1)$oscillations in the number density occur over the coherence time, $\tau_c=h/mv^2$, where $m$ is the particle mass and $v$ is the galactic virial velocity,leading to a reduction in the constraining power of experiments operating ontimescales $T<\tau_c$, due to the unknown global phase. On the other hand ifthe DM is incoherent then no such strong number oscillations occur, since theensemble average over particles in different streams gives an effective phaseaverage. If an experiment detects a signal then the coherent or incoherentnature 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 timesbetween a year and 100 seconds), and can be explored by experiments includingCASPEr, DMRadio, and AION. Coherence may also be measurable at higher masses inthe microwave regime, but I have not explored it.

Measuring the Quantum State of Dark Matter