Multiple ALPs and enhanced echoes

We present a theoretical study of axion echoes in the context of multiple ALP models. We begin by reviewing the single ALP case, deriving the conditions for resonance and echo formation. Starting from a set of N ALPs coupling to the photon, we then derive the relevant echo equations for both coherent and incoherent configurations. In the former case, we show that the echo power scales with N leading to sharper amplification and potentially improving projected bounds discussed earlier in literature. Small mass splittings between the ALPs further increase this amplification, even for a N = 2 case. We also outline the potential experimental implications of our results and discuss prospects for detecting these echoes in a wide range of ALP masses. In the incoherent scenario, we show that the random phases lead to a suppression of the echo power, eventually resulting in observable signals akin to or even weaker than the single ALP case.