Quantum systems of ultracold bosons with customized interparticle interactions

Recent progress in cooling and trapping of polarized clouds of chromium Cr-52, dysprosium Dy-164, and erbium Er-168 opens a roadmap to quantum systems where the shapes of interparticle interactions can be customized. The main purpose of this work is to get deeper insight into the role the overall shape of the interparticle interaction plays in the context of trapped ultracold bosons. We show that strong interparticle repulsion inevitably leads to multihump fragmentation of the ground state. The fragmentation phenomenon is universal-it takes place in traps of different dimensionalities and topologies and for very broad classes of repulsive interparticle potentials. The physics behind this is identified and explained.