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Abstract

This thesis investigates how the emergence of bound states can be used to modify and sense properties of quantum systems. This question is addressed in the context of two different fields – two-dimensional materials and ultracold atomic Rydberg physics. In particular it is studied how charged bound states of electrons and holes in a system of stacked two-dimensional semiconductors can be used to manipulate and control scattering properties of excitons and charge carriers. Here it is found by a first-principle calculation that the mechanism of Feshbach resonances as known from ultracold atoms extends to atomically thin semiconductors with some important differences as, e.g., the necessity to discard the usual definition of the resonance width. Further the use of Rydberg molecules – bound states of atoms and Rydberg atoms – as probes of ultracold atoms is investigated. In particular, a connection between the pair correlation function and the spectral response of the Rydberg-dimer molecule is found. The separation of time and energy scales of the typical system dynamics in ultracold atoms and the molecule formation in addition to their well defined molecular binding length allows to use these molecules as a probe of inter-particle distances in ultracold gases.