From hard-core to soft-core bosons in a shell trap
We study the low-temperature states of a system of spinless bosons trapped in a broad spherical shell. In our virtual (path-integral Monte Carlo) experiments, we specifically examine how the equilibrium structure and overall superfluidity of the system are affected by a change of the interparticle-potential core from hard to increasingly soft. In this manner we bridge the gap between the behaviors of two species of bosons: Helium-like atoms, which self-assemble into ordinary crystalline solids, and Rydberg-dressed atoms, which in simulation form cluster (super)solids. We also vary the particle mass, i.e., the quantumness of the system, so as to modify the relative stability of ``solid'' and fluid states. We thus find a whole spectrum of (finite-size) phases with a curved structure, including multilayer and cluster phases, as well as superfluids and single layer supersolids. In particular, we confirm that supersolids only occur in the presence of clusters. By considering three system sizes (from 60 to 180 particles), but rescaling the trap radius so that the density stays fixed, we verify that supersolid states only exist in the same range of particle masses. Our model serves as a platform to test how emergent properties are modified, in spherical geometry, in the crossover from atoms to dressed atoms.