Fluctuations in atom interferometers as a new tool for dark matter

We propose the use of the super-binomial variance in the count rate of an atom interferometer as a novel signature of dark matter. We show that the dark matter induced shift in this observable is enhanced by N, the number of atoms used per run of the interferometer, and therefore offers sensitivity that is enhanced by orders of magnitude relative to an independent-atom estimate. As an application, we consider dark matter that interacts with electrons, protons, and/or neutrons, via a long-range Yukawa interaction and new constraints on strongly interacting dark matter that thermalizes in the overburden of conventional direct detection experiments. We find that searches for super-binomial variance extend, and complement, existing atom interferometer observables; they are well suited to search for both short- and long-ranged forces.