Pre-Submission Thesis Presentation

Laser-cooled ions, when confined together, self-organize into clusters with distinct symmetries. These clusters provide an exotic, tunable mesoscopic system where the interplay of the trapping potential, Coulomb repulsions, and stochastic laser-ion scattering generates rich, emergent dynamics. In this presentation, I will demonstrate how these clusters emulate the unit-cell dynamics of solid-state materials as well as the fluxional/non-rigid molecular processes, where changes in symmetry play a critical role. We confine clusters of 2 to 6 40Ca+ ions in a three-dimensional (3D) Paul trap, and steer them through a sequence of structural transitions by tuning the trap anisotropy. We classify these transitions as either displacive, characterized by a collective mode instability, or reconstructive, characterized by metastability. We experimentally probe distinct dynamical signatures, including softening of a Higgs-like mode, and hysteresis arising from a catastrophe. We also observe a coincidence of symmetry-breaking transition and a first-order transition, analogous to a thermodynamic “triple-point”. 

Furthermore, the multi-stable energy landscapes, in conjunction with the stochastic noise induced by Doppler-cooling lasers, offer an ideal testbed for studying the kinetics of rare events. We experimentally track real-time inversions of five ions in a square-pyramidal configuration, and observe unambiguous signatures of thermal activation. Numerical analysis reveals a permutation symmetry-assisted “pseudo-rotation” pathway that circumvents the high-barrier canonical umbrella inversion observed in pyramidal molecules. We devise a test to verify this pathway by introducing a mass defect (44Ca+) at the apex; this closes the permutation symmetry-enabled pathway and suppresses thermal activation, realizing a structural analogue of the molecular kinetic isotope effects. Finally, we perform a parameter-free test of Kramers-Langer escape rate theory in a genuine multidimensional setting, allowing for in-situ thermometry of the cluster. These results demonstrate the versatility of 3D trapped-ion clusters for future studies of symmetry-controlled non-equilibrium dynamics and geometric frustration.