In this talk I will do three things. First, I will outline the conditions under which the interaction rate of inelastic processes with a system consisting of N targets scales as N^2. Second, I will present computations of interaction rates for several weakly interacting particles, including the cosmic neutrino background and axion dark matter, and will explain the underlying physics. Third, I will present a concrete experimental protocol using Nuclear Magnetic Resonance that can extract these effects through quantum observables not relying on net energy transfer. This protocol has the potential to significantly accelerate axion and dark photon dark matter searches and extend the reach of existing axion experiments to probe QCD axion-nuclear spin couplings. More broadly, it paves the way for detecting coherent inelastic interactions from other cosmic relics---most notably the cosmic neutrino background---and establishes nuclear-spin-based systems as a new class of quantum, ultra-low-threshold detectors.