Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions-the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.