Classical Analysis of Non-Coherent Dark Matter to Photon Conversion in a Resonant Cavity

Abstract Both axion and dark photon dark matter are among the most promising candidates of dark matter. What we know with some confidence is that they exhibit a small velocity distribution $\delta v\lesssim v\sim 10^{-3}$c. In addition, their mass is small, resulting in a long de Broglie wavelength and a high particle number density. Their phase space distribution contains many uncertainties, so they could give rise to either a coherent or noncoherent wave on the laboratory scale. In this paper, we demonstrated that a resonant cavity can enhance noncoherent axion-to-photon or dark photon-to-photon transitions, and the resulting power is the same as in the coherence case. The classical picture explanation is that a cavity can resonant with multiple different sources simultaneously. This aligns with the quantum perspective, where the cavity boosts dark matter particles transitioning into photons similarly to the Purcell effect. This effect increases the density of states near resonance, regardless of the coherence nature of dark matter. Certainly, the induced microwave signals in a cavity are also non-coherent, and in such case, a single-photon readout may be required.