An open EFT for dark matter searches with matter-wave interferometers

Matter-wave interferometers (MWIs) are a genuine quantum probe of dark matter (DM), being sensitive to DM-induced phase shifts and loss of contrast. Treating the interferometer as an open quantum system and the dark sector as its environment, we derive an open EFT to study these signatures using the Schwinger-Keldysh formalism. Starting from a microscopic theory, we derive the interferometer's effective action, which we then project onto the many-body worldline sectors relevant for atom interferometers and MWIs employing mesoscopic objects, i.e., composite-particle interferometers (CPIs). This construction clarifies the heavy-probe limit and organizes phase shifts and decoherence as distinct real-time components of the influence action: the retarded kernel controls the causal response of the environment, while the Keldysh kernel controls environmental fluctuations and hence loss of contrast. At leading order, these kernels reduce to: (i) DM bubble diagrams in the case of four-point interactions, and (ii) dressed in-medium mediator propagators in the case of long-range interactions, where the dressing is provided by the DM environment. Within this framework, we study the signatures of elastic spin-independent sub-GeV DM scattering off nucleons and find that: (i) owing to Bose enhancements below the DM wave-particle boundary, ambitious CPIs could probe Higgs-portal DM with mass below 1 eV in an unexplored region of model space; (ii) for DM coupled to nucleons via a light hadrophilic scalar, the DM background can drive the mediator's in-medium mass tachyonic over much of parameter space; outside these regions, CPIs could probe provide powerful probes of light DM.