Symmetry-Controlled Thermal Activation in Pyramidal Coulomb Clusters: Testing Kramers-Langer Theory

Laser-cooled ions confined in electromagnetic traps provide a unique, tunable mesoscopic system where the interplay of the trapping potential, nonlinear Coulomb interactions, and laser-ion scattering generates rich, collective dynamics. In this work, we engineer thermally activated switching between two oppositely oriented, square-pyramidal configurations of five laser-cooled ions in a Paul trap. For identical ions (^{40}Ca^{+}), the inversions proceed via a Berry pseudorotation mechanism with a low activation barrier, enabled by the permutation symmetry, in contrast to the umbrella inversion observed in ammonia. The inversion rates obtained from experiments and the Langevin dynamics simulations are accurately captured by the multidimensional Kramers-Langer theory, enabling thermometry of the Doppler-cooled ion cluster at 1.86±0.03  mK. By substituting the apex ion with a heavier isotope (^{44}Ca^{+}), we break the permutation symmetry and observe a suppression of thermally activated inversions. Numerical analysis reveals that this symmetry breaking closes the low-barrier channel, forcing the system to invert through a high-barrier turnstile rotation. Thus, we demonstrate a structural analog of molecular kinetic isotope effects, establishing trapped ions as a versatile platform to explore symmetry-controlled collective dynamics.