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arXiv:1909.01511 · Physical Review Letters

Quantum Walks of a Phonon in Trapped Ions

Masaya Tamura, Takashi Mukaiyama, Kenji Toyoda

Published May 19, 2020• 49 citations
arXivHTMLPDF

Abstract

We report the observation of the quantum walks of a phonon, a vibrational quantum, in a trapped-ion crystal. By employing the capability to prepare and observe the localized wave packet of a phonon, the propagation of a single radial local phonon in a four-ion linear crystal is observed with single-site resolution. The results show an agreement with numerical calculations, indicating the predictability and reproducibility of the phonon system. These characteristics may contribute advantageously in the advanced studies of quantum walks, as well as boson sampling and quantum simulation.

DOI
10.1103/physrevlett.124.200501

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Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 μμμm on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.
We systematically investigate local phonon hopping in the radial direction of a linear trapped-ion string. We measure the decay of hopping as a function of key trap parameters and analyze the results in terms of the decay time and the number of oscillations. We attribute the loss of coherence to nonlinear coupling between different modes. Despite quantitative differences, the overall trends in our numerical simulations are similar to those of the experimental results. This work establishes a method for evaluating phonon hopping coherence and provides insight into the underlying decoherence mechanisms.