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We consider the quench of an atomic impurity via a single Rydberg excitationin a degenerate Fermi gas. The Rydberg interaction with the background gasparticles induces an ultralong-range potential that binds particles to formdimers, trimers, tetramers, etc. Such oligomeric molecules were recentlyobserved in atomic Bose-Einstein condensates. In this work, we demonstrate witha functional determinant approach that quantum statistics and fluctuations haveobservable spectral consequences. We show that the occupation of molecularstates is predicated on the Fermi statistics, which suppresses molecularformation in an emergent molecular shell structure. At large gas densities thisleads to spectral narrowing, which can serve as a probe of the quantum gasthermodynamic properties.

Rydberg impurity in a Fermi gas: Quantum statistics and rotational blockade