Abstract: We will discuss the formation and instabilities of quantum droplet and bubble phases arising in two-component attractively interacting bosonic mixtures. Insights regarding the interplay of atom and interaction imbalance as well as the impact of dimensionality giving rise, for instance, to a transition from mixed droplet-gas to pure self-bound states will be elucidated. These phases are addressed within the suitable extended Gross-Pitaevskii framework incorporating the first-order Lee-Huang-Yang quantum correction. An effective model based on the established Lee-Huang-Yang theory is constructed and found to provide qualitative analytical predictions. The stability properties of these configurations will be analyzed resorting to the Bogoliubov-de-Gennes excitation spectrum. Additionally, the two-body correlation patterns of the above-mentioned structural phase transitions will be explicated. Finally, a plethora of applications will be provided ranging from the snake instability of dark soliton stripes, to the generic stability of kink configurations and the destabilization of oblique dispersive shock-waves.

We will then extend the discussion to emergent many-body phenomena in ultracold chemistry, where coherent reactions provide an additional mechanism for engineering quantum phases and dynamics. Specifically, we will consider quantum degenerate atom-molecule mixtures in which two-body Fano-Feshbach conversion competes with coherent three-body recombination. When the latter becomes prominent, a structural deformation from a second-order to a first-order quantum phase transition of the atom-molecule mixture takes place. This process originates from a double-well structure of the ensuing energy landscape and it is accompanied by bistability, molecular metastability, and enhanced atom-molecule entanglement. To probe the dynamical signatures of the metastable molecular condensate, we will utilize quenches across the relevant phase boundaries, revealing how coherent few-body reaction processes can be exploited to steer chemical reactions at ultralow temperatures.