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 ($^{40}\mathrm{Ca}^{+}$), the inversions proceed via a \textit{Berry pseudo-rotation} mechanism with a low activation barrier, enabled by the permutation symmetry, in contrast to the \textit{umbrella inversion} observed in ammonia. The experimentally measured inversion rates, spanning two orders of magnitude, are accurately captured by the multidimensional Kramers-Langer theory, enabling thermometry of the Doppler-cooled ion cluster at $1.8 \pm 0.1$ mK. By substituting the apex ion with a heavier isotope ($^{44}\mathrm{Ca}^{+}$), 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 \textit{turnstile rotation}. Thus, we demonstrate a structural analogue of molecular kinetic isotope effects, establishing trapped ions as a versatile platform to explore symmetry-controlled collective dynamics.