911³Ô¹Ï

Synopsis

The linear-zigzag transition in trapped-ion crystals provides a highly controllable system for studying structural phase transitions in the quantum regime. Near the critical point, the transition is described by an effective double-well potential associated with two symmetry broken zigzag configurations. Studies of quantum tunnelling and coherent superpositions of these structural states require a quantitative understanding of the transition near criticality and of symmetry-breaking effects that can bias the zigzag double-well potential. This thesis investigates these effects through Raman spectroscopic measurements of small trapped-ion crystals near their motional ground state. Spectroscopy of the transverse zigzag mode is used to characterize the effective double-well potential and to directly measure intrinsic symmetry-breaking terms in the effective potential. Measurements performed for ion crystals containing three to five ions reveal that the intrinsic bias decreases rapidly with increasing ion number, resulting in a nearly symmetric double-well potential for fiveion crystals. A theoretical framework relating trap imperfections to odd-order terms in the effective potential, combined with electrostatic simulations, is developed and used to quantitatively connect measured bias coefficients to realistic electrode deformations and to identify likely sources of the observed bias. In addition, spectroscopic measurements of the critical aspect ratio near the motional ground state reveal systematic shifts of approximately 1% from predictions under the pseudopotential approximation. Comparison with theoretical models incorporating micromotion-induced shifts of the zigzag-mode frequency yields quantitative agreement with the observed critical-point shifts, providing experimental validation of beyond-pseudopotential effects in the linear-zigzag transition. Together, these results establish a quantitative understanding of both intrinsic symmetry breaking and systematic shifts of the critical point of the linear-zigzag transition. The demonstrated suppression of intrinsic bias with increasing ion number and the improved characterization of the transition near criticality provide a foundation for future investigations of quantum tunnelling and coherent superpositions of structural states in trapped-ion crystals.

For Zoom link info, please contact Lindiwe Coyne at physgrad@sfu.ca.