Susanna L. Todaro

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 $μ$m 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.

Coherent storage of quantum information is crucial to many quantum technologies. Long coherence times have been demonstrated in trapped-ion qubits, typically using the hyperfine levels within the ground state of a single ion. However, recent research suggests qubits encoded in metastable states could provide architectural benefits for quantum information processing, such as the possibility of effective dual-species operation in a single-species system and erasure-error conversion for fault-tolerant quantum computing. Here we demonstrate long-lived encoding of a quantum state in the metastable states of a trapped ion. By sympathetically cooling with another ion of the same species and constantly monitoring for erasure errors, we demonstrate a coherence time of 136(42) seconds with a qubit encoded in the metastable $5D_{5/2}$ state of a single $^{137}$Ba$^+$ ion. In agreement with a model based on empirical results from dynamical-decoupling-based noise spectroscopy, we find that dephasing of the metastable levels is the dominant source of error once erasure errors are removed.