Angular momentum and shapes of rotating quantum droplets.

ABSTRACT: Self-bound quantum droplets, resulting from the balance between attractive and repulsive forces between their atomic components, appear in different physical scenarios, the prototypes being liquid droplets made of superfluid Helium-4. Recently, a new kind of quantum droplets have been found using a bosonic mixture of ultracold atoms, whose stability results from the interplay between the inter-species attractive mean-field energy and the repulsive term representing a beyond-mean-field correction due to quantum fluctuations. Being a mixture of Bose-Einstein condensates, quantum droplets are likely superfluid. Thus, when they are set into rotation, the angular momentum can only be stored in the form of quantized vortices and/or capillary waves. In the case of superfluid Helium-4, the interplay between vortices and capillary waves results in droplet shapes surprisingly close to those of classical liquid droplets rotating with the same angular velocity. In the case of quantum droplets made of Bosonic mixtures, such interplay remains to be uncovered. The scope of this thesis is to theoretically study the stability and appearance of rotating self-bound nanodroplets made of Bosonic binary mixtures using numerical simulations based on Density Functional Theory, to unveil the interplay between the superfluid nature of the system and their shapes.