Symmetry-controlled thermal activation in pyramidal Coulomb clusters: Testing Kramers-Langer theory

Abstract

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.

11 pages, 8 figures

References in corpus (15)

• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Symmetry Breaking and Topological Defect Formation in Ion Coulomb Crystals
• A simple and effective Verlet-type algorithm for simulating Langevin dynamics
• Observation of the Kibble-Zurek scaling law for defect formation in ion crystals
• Cryogenic Trapped-Ion System for Large Scale Quantum Simulation
• Direct Measurement of Kramers Turnover with a Levitated Nanoparticle
• Modes of Oscillation in Radiofrequency Paul Traps
• Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal
• Fast thermometry for trapped ions using dark resonances
• Raman cooling and heating of two trapped Ba+ ions
• Transition path dynamics of a nanoparticle in a bistable optical trap
• Doppler cooling of a Coulomb crystal
• Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
• Observing the dynamics of octupolar structural transitions in trapped-ion clusters
• Modular variable laser cooling for efficient entropy extraction