  We consider the quench of an atomic impurity via a single Rydberg excitation
in a degenerate Fermi gas. The Rydberg interaction with the background gas
particles induces an ultralong-range potential that binds particles to form
dimers, trimers, tetramers, etc. Such oligomeric molecules were recently
observed in atomic Bose-Einstein condensates. In this work, we demonstrate with
a functional determinant approach that quantum statistics and fluctuations have
observable spectral consequences. We show that the occupation of molecular
states is predicated on the Fermi statistics, which suppresses molecular
formation in an emergent molecular shell structure. At large gas densities this
leads to spectral narrowing, which can serve as a probe of the quantum gas
thermodynamic properties.
