  Immersing a mobile impurity into a many-body quantum system represents a
theoretically intriguing and experimentally effective way of probing its
properties.In this work, we study the polaron spectral function in various
environments, within the framework of Fermi-Hubbard models. Inspired by
possible realizations in cold atoms and semiconductor heterostructures, we
consider different configurations for the background Fermi gas, including
charge density waves, multiple Fermi seas and pair superfluids. While our
calculations are performed using an exact-diagonalization approach, hence
limiting our analysis to systems of few interacting Fermi particles, we
identify robust spectral features supported by theoretical results. Our work
provides a benchmark for computations based on mean-field approaches and reveal
surprising features of polaron spectra, inspiring new theoretical
investigations.
