Title: Phenomenology of a Rydberg impurity in an ideal Bose Einstein condensate

Abstract: We investigate the absorption spectrum of a Rydberg impurity immersed in and interacting with an ideal Bose-Einstein condensate. Here, the impurity-bath interaction can greatly exceed the mean interparticle distance; this discrepancy in length scales challenges the assumptions underlying the universal aspects of impurity atoms in dilute bosonic environments. Our analysis finds three distinct parameter regimes, each characterized by a unique spectral response. In the low-density regime, we find that the Rydberg impurity is dressed by the surrounding bath similarly to the known Bose polaron. Transitioning to intermediate densities, the impurity response, given by sharp quasiparticle peaks, fragments into an intricate pattern bearing the hallmarks of a diverse molecular structure. Finally, at high density, a universal Gaussian response emerges as the statistical nature of the bath dominates its quantum dynamics. We complement this analysis with a study of an ionic impurity, which behaves equivalently. Our exploration offers insights into the interplay between interaction range, density, and many-body behavior in impurity systems.