Solitons and polarons in ultracold bosonic mixtures

The realization of multicomponent systems offers a natural playground to observe nonequilibrium effects in a more general framework. Restricting to two-component BECs, one notices already a rich variety of phases in the ground state. In purely repulsive mixtures, one observes a homogeneous superfluid or a phase separation when inter-species repulsion overcomes the intra-species interaction strength. In the attractive regime a series of recent experiments showed the formation of dilute self-bound droplet states in a two-component BEC both in a tight optical waveguide and in free space, closely following the theoretical predictions. In the quasi one-dimensional geometry, upon varying the mean-field interaction from the weakly to the strongly attractive regime, one observes a smooth crossover between bright soliton states and self-bound droplets. In the first part we investigate the quench dynamics of a two component Bose mixture and study the onset of modulational instability, which leads the system far from equilibrium. Analogous to the single-component counterpart, this phenomenon results in the creation of trains of bright solitons. In the second part I will discuss the properties of impurities in uniform and self-bound states of heteronuclear mixtures inspired by recent experiments. Finally, I will focus on the formation of exotic bound states for an impurity interacting with a self-bound droplet.