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

In recent years, quantum simulation has emerged as a promising approach for elucidating many-body quantum phenomena that are intractable with classical computational methods. Highly controllable quantum platforms such as superconducting circuits, neutral-atom arrays, and trapped ions have been actively employed for this purpose. Among them, the trapped-ion system is particularly attractive because it combines long coherence times with precise, site-resolved control over individual ions.

In quantum simulation using trapped ions, both the internal states (spins) and the vibrational modes (phonons) can be employed as effective simulation resources. The internal state has been widely used in quantum information processing as ideal qubits. On the other hand, vibrational modes possess multiple quantum levels and can also be utilized as effective computational resources in quantum information and quantum simulation. However, in large ion arrays, controlling the quantum states of vibrational modes is technically challenging, and experimental studies at the single-phonon level have been limited. We experimentally observed the propagation of a single phonon in a 10-ion array and compared the results with theoretical analysis. We found that the inhomogeneous ion spacing, inherent in harmonic trapping potentials, gives rise to characteristic phonon propagation behavior. In this presentation, we report on these results.