Quantum scar, classical localisation, and Berry-Robnik statistics for three Rydberg atoms in a circular trap

We consider three interacting bosonic particles in a circular trap. This system is within experimental reach owing to recent advances in Rydberg atom trapping. Firstly, we show that the energy levels of the quantum system are well described by a Berry-Robnik distribution, reflecting the mixed nature of the phase space of the corresponding classical system. Secondly, we characterise two different mechanisms impeding ergodicity in this system. First, the system exhibits a quantum scar in Heller's sense, due to a classically unstable periodic trajectory. The scar impacts multiple quantum levels, forming towers of scarred states whose energies we analyse using Gutzwiller's trace formula. Second, classical localisation occurs near stable periodic trajectories. We have characterised the energies and wavefunctions of the resulting localised quantum states using the Einstein-Brillouin-Keller theory, highlighting the impact of discrete symmetries, including bosonic exchange symmetry. Our EBK results are in excellent agreement with our full-fledged finite-element numerics.