The behaviour of a mobile impurity particle interacting with a quantum-mechanical medium is of fundamental importance in physics. Ultracold atomic gases have greatly improved our understanding of the impurity problem owing to the high degree of control over experimental parameters such as interactions and atom population. I will discuss recent theoretical and experimental progress in exploring the properties of impurities interacting with a fermonic medium. In particular, I will present a theoretical approach for describing the coherent non-perturbative quantum evolution following a quench of the impurity-medium interactions.

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