Exploring Quantum Aspects of Dark Matter Axions and Dark Photons Transitioning to Photons in a Resonant Cavity

When axion cold dark matter interacts with a static magnetic field, it can be converted to photons with energy near the axion's mass. Classical analysis shows that incorporating a resonant cavity significantly enhances this conversion rate, forming the basis for many experiments aimed at detecting dark matter axions. However, one might ask: Does the axion-photon conversion rate increase for a single axion-photon transition? Answering this question could lead to optimizing the search for axions by integrating quantum measurement techniques. In this paper, we demonstrate that at the quantum level, single axion-photon transitions are amplified by the cavity quality factor $Q$. Furthermore, the coherence of dark matter waves is unnecessary during the measurement. The underlying principle is similar to the Purcell effect. Additionally, we provide an analysis of the scenario involving dark photon dark matter.