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Immersing a mobile impurity into a many-body quantum system represents atheoretically intriguing and experimentally effective way of probing itsproperties.In this work, we study the polaron spectral function in variousenvironments, within the framework of Fermi-Hubbard models. Inspired bypossible realizations in cold atoms and semiconductor heterostructures, weconsider different configurations for the background Fermi gas, includingcharge density waves, multiple Fermi seas and pair superfluids. While ourcalculations are performed using an exact-diagonalization approach, hencelimiting our analysis to systems of few interacting Fermi particles, weidentify robust spectral features supported by theoretical results. Our workprovides a benchmark for computations based on mean-field approaches and revealsurprising features of polaron spectra, inspiring new theoreticalinvestigations.

Polaron spectroscopy of interacting Fermi systems: insights from exact diagonalization