Beyond Mean-Field Effects in Bose-Einstein Condensates: Supersolids, Droplets and Polarons

The progress in cooling and control of ultracold quantum gases and their mixtures allowed for the engineering of new states of matter. Ultradilute quantum liquid of a binary mixture of Bose-Einstein condensates (BECs) at the border of stability is one example. It allows for formation of finite-size, self-bound quantum droplets. Another possible mechanism of droplet formation is through long-range dipolar interactions. In this talk I will present an overview of these phenomena, and discuss one-dimensional ultradilute quantum liquids in binary BECs in the context of their collective excitations and Josephson dynamics. I will also consider a mobile impurity and its out-of-equilibrium properties, such as the stationary momentum at long times, which is nonzero due to the superfluid nature of the medium, the effective mass and the oscillatory dynamics of the momentum transfer between the impurity and the condensate.