Impurity problems have been at the forefront of research in condensed matter physics for several decades. When an impurity is immersed into an environment, it changes its properties due to its interactions with the surrounding medium. The impurity becomes dressed by many-body excitations and forms a quasiparticle, the polaron. Depending on the character of the environment and the form of interactions, different types of polarons are created. In this talk, I will review recent experimental and theoretical progress on studying the many-body physics of polarons in ultracold atomic systems. I will then focus in particular on Rydberg excitations in Bose-Einstein condensates and show that such Rydberg impurity excitations present a new frontier in impurity research. Here vastly different energy scales compete, signified in deeply bound Rydberg molecules of mesoscopic size . This situation poses a new challenge for theoretical physics and necessitates the confluence of methods ranging from mesoscopic to atomic physics. In recent theoretical work , we develop a novel many-body theory for the non-equilibrium dynamics of impurity excitations in Bose gases. In this talk, we report the spectroscopic observation of the predicted Rydberg polarons  in a Bose-Einstein condensate of Strontium atoms which is in excellent agreement with theoretical predictions. This novel type of polaron is created by excitation of Rydberg atoms in a Strontium Bose-Einstein condensate, and it is distinguished by the occupation of a large number bound molecular states. The crossover from few-body bound molecular oligomers to many-body polaron features is described with a functional determinant theory that solves an extended Fröhlich Hamiltonian for an impurity in a Bose gas. Our time-dependent formalism is not restricted to Rydberg systems but can be applied to various impurities in bosonic and fermionic environments and opens new possibilities to study impurity dynamics in mesoscopic systems [4,5].
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