Axially confined binary quantum droplets: ground states and central vortices

Ultracold miscible mixtures of bosonic gases have been observed to form quantum droplet states stabilized by beyond-mean-field quantum fluctuations. Here we study the properties of the droplets when subjected to harmonic trapping in one dimension, using a combination of numerical, variational and analytical approaches. We map out the phase diagram between bound droplets and the unbound gas state and the form of the ground states. We additionally consider how the droplet solutions are modified by the presence of a central vortex and use these results to estimate the critical rotation frequency for vortices to be energetically favored. Our work helps to understand the physics of self-bound droplets and vortex droplets in flattened geometries.