Superradiant Interactions of the Cosmic Neutrino Background, Axions, Dark Matter, and Reactor Neutrinos

In this paper we do three things. First, we outline the conditions under which the interaction rate of inelastic processes that change the internal state of a system of $N$ targets scales as $N^2$. This is an effect distinct from coherent elastic scattering, but with the same scaling. Second, we compute rates for such processes for various weakly interacting particles. Finally, we point to potential quantum observables for these processes, beyond energy exchange. Maximal coherence in inelastic processes is achieved when the targets are placed in an equal superposition of the ground and excited states. These coherent inelastic processes are analogous to Dicke superradiance, and we thus refer to them as superradiant interactions. We compute the superradiant interaction rates for the Cosmic Neutrino Background (C$\nu$B), dark matter scattering and absorption, and late-universe particles, such as reactor neutrinos, when the two-level system is realized by nuclear or electron spins in a magnetic field. The rates can be sizeable on macroscopic yet small targets. For example, the C$\nu$B interacts with a rate of $\mathcal{O}(\text{Hz})$ when scattering off a 10~cm liquid or solid-state density spin-polarized sphere, a $\mathcal{O}(10^{21})$ enhancement compared to the incoherent contribution. For QCD axion dark matter, similar rates can be achieved with much smaller samples, $N \sim \mathcal{O}(10^{15})\left(\frac{m}{2\times 10^{-8}~\text{eV}}\right)^{-1/2}$, where $m$ is the axion mass. Using the Lindblad formalism, we show that these superradiant interactions can manifest as a source of noise on the system. This points to new observables, sensitive to the sum of the excitation and de-excitation rates, and can be viewed as introducing diffusion and decoherence to the system. The effects presented in this paper may point to a new class of ultra-low threshold detectors.