Emergent phenomena in quantum mixtures: from ultra-cold gases to light-matter systems

Quantum mixtures of ultra-cold atoms are exceptional platforms which allow to investigate a huge variety of phenomena owing to the exquisite control of interactions between atoms. We present here a theoretical investigation of some distinctive phenomena emerging in these systems which highlight their quantum nature. Balanced mixtures at sufficiently low temperatures are superfluid and, when set into rotation, they display topological excitations in the form of quantum vortices. In many physical systems, especially in quantum mixtures, the scenario is richer as the vortex core is filled, either deliberately or accidentally, by particles and then stable massive vortices appear. The finite inertial mass has an unmistakable dynamical signature in the trajectory of vortices in two-dimensional superfluids. On the one hand, in bosonic mixtures massive vortices may appear in the immiscible regime where one (majority) component features topological excitations and the other (minority) component localizes at the vortex cores. On the other hand, in Fermi superfluids vortices are intrinsically massive, due to the presence of normal component at the vortex core. Together with dissipative effects, the core mass is expected to affect the collective properties of many-vortex systems, such as providing a stabilization mechanism for usual shear-flow instabilities that have been currently investigated in experiments. In the strongly imbalanced regime, quantum mixtures offer a unique viewpoint on the well-known impurity problem. In particular, the strongly-interacting system made of an impurity atom in a Fermi sea can be described in terms of a Fermi polaron, the prototypical realization of Landau's fundamental concept of quasiparticle. We study the behaviour of the moving Fermi polaron, finding a breakdown of the effective mass description at finite momentum which finds a solid confirmation in a cold-atom experiment. A novel type of quantum liquid may also appear in ultra-cold bosonic mixtures from a competition between interactions. When the mean-field attraction is balanced by a repulsion induced by quantum fluctuations, the system stabilizes into a self-bound configuration, known as quantum droplet. While this physics has been explored in the context of quantum gases, we predict here the existence of a similar droplet phase in a solid-state system with light-matter interactions. We consider a spin mixture of exciton-polaritons, hybrid light-matter quasiparticles formed from the strong coupling between excitons (bound electron-hole pairs) and photons in a semiconductor microcavity. This exotic phase could open an alternative avenue to achieve the long-sought quantum polaritonic regime.