Measuring the Quantum State of Dark Matter

TL;DR

This paper proposes a method to determine whether ultralight bosonic dark matter is in a coherent or incoherent quantum state by analyzing time series data from detection experiments, which has implications for understanding dark matter properties.

Contribution

It introduces a simple, explicit approach to distinguish the quantum coherence state of dark matter using time series analysis, encouraging experimental exploration.

Findings

Coherent dark matter shows oscillations in number density over the coherence time.

Incoherent dark matter lacks strong number oscillations due to phase averaging.

The method applies to dark matter masses between 10^{-17} eV and 10^{-11} eV.

Abstract

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.