Observing dynamics of distinct structural transitions in trapped-ion clusters

Interacting many-particle systems can self-organize into a rich variety of crystalline structures. While symmetry provides a powerful framework for predicting whether structural transitions between crystal states are continuous or discontinuous, collective lattice dynamics offer complementary insights into the microscopic mechanisms that drive these transitions. Trapped laser-cooled ions present a pristine and highly controllable few-body system for studying this interplay of symmetry and dynamics. Here, we use real-time fluorescence imaging while deforming the trap potential to observe a variety of structural transitions in three-dimensional unit-cell-sized ion clusters. We probe their distinct dynamical signatures: mode softening indicating a structural instability at a symmetry-breaking continuous transition, stochastic switching between stable structures at a discontinuous transition, and hysteresis near a spinodal point. We also observe a remarkable triple point-like feature where a discontinuous symmetry-changing transition and a continuous symmetry-breaking transition occur simultaneously. Analytical calculations based on symmetry considerations and numerical analysis of collective modes provide a comprehensive understanding of the observed dynamics. Our results demonstrate that tunable Coulomb clusters serve as a versatile platform to elucidate the interplay between symmetry, energy landscapes, and dynamical pathways in structural transitions.