Quantum propagation of vibrational excitation in harmonically confined trapped-ion crystal

Vibrational excitations, or phonons, in trapped ions serve as useful resources for quantum information processing, including quantum simulation and computing. Localized excitations of ions' vibrational motion (local phonons) can be used for simulating quantum particles that propagate over a system. Here, we experimentally investigate the propagation of a localized vibrational excitation in a one-dimensional trapped-ion crystal. A 10-ion crystal confined in a harmonic potential is used. It is found that inhomogeneity in the spacing between the ions leads to characteristic behaviors such as adjacent hopping and global movement. A comparison of the experimental results with numerical simulations shows agreement up to fine details. The system explored here may be extended to many-body systems of bosonic particles as well as more complex quasiparticles.