Vertical Shuttling Protocols for Trapped Ions in Multi-Rail, Multi-Zone Surface Ion Trap Architectures

We investigate optimized vertical ion-shuttling protocols for trapped-ion applications across a range of ion-trap experiments, including three-dimensional gradient-measurement sensors, on-chip ion fluorescence collection and imaging, improved laser accessibility, and quantum information processing. In this work, we focus on minimizing motional energy gain during ion transport. Our findings indicate that anomalous heating becomes the dominant limiting factor only for shuttling durations exceeding $500~μ\mathrm{s}$, whereas the final motional excitation is strongly dependent on the selected transport protocol. Using a recently measured heating rate of $(3.1 \pm 0.35)$ quanta/ms at an ion--surface separation of $134 \pm 1.5~μ\mathrm{m}$, we demonstrate that the motional excitation can be restricted to fewer than eight quanta when the ion is vertically displaced by $86~μ\mathrm{m}$ from its initial position. These results enable adiabatic shuttling within $0.5~\mathrm{ms}$, thereby meeting the operational requirements for high-fidelity quantum sensing and coherent control.