Fermionic matter-wave quantum optics with cold-atom impurity models

Motivated by recent cold-atom realizations of matter-wave waveguide QED, we study simple fermionic impurity models and discuss fermionic analogs of several paradigmatic phenomena in quantum optics, including formation of nontrivial bound states, (matter-wave) emission dynamics, and collective dissipation. For a single impurity, we highlight interesting ground-state features, focusing in particular on real-space signatures of an emergent length scale associated with an impurity screening cloud. We also present non-Markovian many-body effects in the quench dynamics of single- and multiple-impurity systems, including fractional decay around the Fermi level and multiexcitation population trapping due to bound states in the continuum.