Emerson Luna Dark Matter Interferometry Joshua W. Foster, Yonatan Kahn, Rachel Nguyen, Nicholas L. Rodd, Benjamin R. Safdi Hide abstract | Show figures | Show BibTeX | Show discussion | View PDF | 2009.14201v2 The next generation of ultralight dark matter (DM) direct detection experiments, which could confirm sub-eV bosons as the dominant source of DM, will feature multiple detectors operating at various terrestrial locations. As a result of the wave-like nature of ultralight DM, spatially separated detectors will each measure a unique DM phase. When the separation between experiments is comparable to the DM coherence length, the spatially-varying phase contains information beyond that which is accessible at a single detector. We introduce a formalism to extract this information, which performs interferometry directly on the DM wave. In particular, we develop a likelihood-based framework that combines data from multiple experiments to constrain directional information about the DM phase space distribution. We show that the signal in multiple detectors is subject to a daily modulation effect unique to wave-like DM. Leveraging daily modulation, we illustrate that within days of an initial discovery multiple detectors acting in unison could localize directional parameters of the DM velocity distribution such as the direction of the solar velocity to sub-degree accuracy, or the direction of a putative cold DM stream to the sub-arcminute level. We outline how to optimize the locations of multiple detectors with either resonant cavity (such as ADMX or HAYSTAC) or quasistatic (such as ABRACADABRA or DM-Radio) readouts to have maximal sensitivity to the full 3-dimensional DM velocity distribution. Authors' comments: 25 pages, 9 figures, animation available at https://github.com/joshwfoster/DM_Interferometry, updated to published version