Multiband and array effects in matter-wave-based waveguide QED

Recent experiments on spontaneous emission of atomic matter waves [Krinner et al., Nature (London) 559, 589 (2018); Stewart Phys. Rev. Research 2, 043307 (2020)] open a window into the behavior quantum emitters coupled to waveguide. Here we develop an approach based infinite products study this system theoretically, without need approximate band dispersion relation We solve for one-dimensional array one, multiple, and number compare with experiments. This leads detailed characterization decay spectrum, family in-gap bound states, mechanisms enhanced Markovian different from superradiance, emergence matter-wave polaritons.