Vector Wave Dark Matter and Terrestrial Quantum Sensors

Abstract: (Ultra)light spin-$1$ particles -- dark photons -- can constitute all of dark matter (DM) and have beyond Standard Model couplings. This can lead to a coherent, oscillatory signature in terrestrial detectors that depends on the coupling strength. We provide a signal analysis and statistical framework for inferring the properties of such DM by taking into account (i) the stochastic and (ii) the vector nature of the underlying field, along with (iii) the effects due to the Earth's rotation. Owing to equipartition, on time scales shorter than the coherence time the DM field vector typically traces out a fixed ellipse. Taking this ellipse and the rotation of the Earth into account, we highlight a distinctive three-peak signal in Fourier space that can be used to constrain DM coupling strengths. Accounting for all three peaks, we derive latitude-independent constraints on such DM couplings, unlike those stemming from single-peak studies. We apply our framework to the search for ultralight $B - L$ DM using optomechanical sensors, demonstrating the ability to delve into previously unprobed regions of this DM candidate's parameter space.