Development of a Phonon Toolbox on a Surface Electrode Trap

We report on our current experimental progress towards using a surface electrode trap for quantum simulation with $\text{Yb}^+$ ions. Currently, we are developing a toolbox for creating, manipulating and reading out phonon occupations in all normal modes of a three ion chain. Using shuttling, composite pulse sequences, and state distillation, we prepare given phonon number-states in these modes and show that these states preserve spin-motion coherence. The prepared state is read out either through a single sideband operation or through a STIRAP process. The sideband operation gives a binary measurement of phonon(s) vs. no phonon occupation; the STIRAP process is sensitive to the number-state occupation. We also engineer coherent couplings between normal modes through optical dipole forces, manipulating the prepared state to sample interacting Bosonic modes.