Measuring the Quantum State of Dark Matter

Understand

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.