Among the fundamental symmetry classes of quantum chaotic systems in Dyson's threefold way, the symplectic class is rarely observed in nature. Characterized by the strongest possible level repulsion in the energy spectrum, the symplectic symmetry class also implies a double (Kramers) degeneracy of levels. Studying the spectral statistics of three quantum particles (identical bosons or mass-imbalanced fermions) in a harmonic trap, we find numerical evidence for strong level repulsion in the regime of weak contact interactions. While the statistical indicators are consistent with quantum chaos in systems with symplectic symmetry, the absence of Kramers degeneracy rules out this symmetry. In the strongly interacting unitary limit either Poissonian or stick statistics are observed (depending on commensurability of the mass ratio) indicating regular dynamics. The transition between the regular and chaotic regimes as a function of interaction strength is well described by the Rosenzweig-Porter model. The system can be realized with cold neutral atoms in microtraps or in optical lattices.

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• Few-body systems
• Quantum chaos
• Ultracold collisions
• Ultracold gases
• Random matrix theory