Quantum droplet molecules in Bose-Bose mixtures

We investigate the interaction between two self-bound droplets separated by a finite distance in one-dimensional symmetric Bose-Bose mixtures. The main objective is to identify the regime where such two identical droplets support a stable bound-state known as droplet molecule. Our analysis is based on the generalized Gross-Pitaevskii equation, combining cubic and quadratic nonlinearities, which is solved by both variational method and numerical simulation. We calculate in particular the droplet-droplet interaction potential, the binding energy, the density profiles and the width of the droplet. It is shown that the developed variational approximation properly predicts the stability and the static and dynamic properties of such droplet molecules. Our results reveal that under appropriate adjustment of the system parameters such as the droplet separation and the number of atoms, a stable bound-state is formed in the regime of Gaussian-like shape. Nevertheless, in the flat top regime, the two droplets merge into one, leading to an unstable molecule.