Collective excitations in two-component ultracold quantum matter

In this paper, we have reviewed a range of theoretical works on collective oscillations in two-component ultracold quantum gases. It is shown that in two-component systems, two key collective modes are generated: a density mode and a spin mode. Using different prototypes of cold bosonic systems as examples, it is shown how these modes at certain parameter values can get converted into Goldstone modes: indicating criticality. Additionally, emergence of roton modes (and roton softening, too) is discussed in the context of two component boson-boson and boson-fermion mixtures, with a particular focus on striped phases. In the fermionic front, it is demonstrated that two-species systems lead to population-imbalanced exotic phases like FFLO and breached pair; and the collective excitations carry very important information about those structures: like the amount of imbalance present, exact pairing structure, etc. Since it is often difficult to resolve such structures in direct experiments, a study of the collective oscillations can prove to be very useful as indirect probes.