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Cornell University

Katz Lab

Setting atoms & ions in |motion>

Programmable Quantum Spin Crystals

One of the most fascinating properties of quantum materials is their ability to occupy a nontrivial state that exhibits unique quantum features with no classical parallel. The many-body quantum properties emerge as a function of the microscopic interactions between the atoms forming the crystal. Trapped ions provide a pristine platform that, with tightly focused laser fields targeting individual atoms, enables the efficient engineering of interaction graphs in low-dimensional crystals. This allows for the preparation of exotic phases of matter, such as one exhibiting Continuous Symmetry Breaking—a phase that features long-range order across the crystal but lacks a preferred direction. To the right shown measurement of such phase associated with the ground state of the long-range XY Hamiltonian in one dimension.
Long-range, macroscopic order in the Continuous Symmetry Breaking Phase. Top: Iteraction between spins in a one-dimensional crystal with 23 sites, as a function of their distance. Left: Long-range interaction. Right: Short-range interaction. Bottom: Measured (connected) correlation function near the ground state of the XY Hamiltonian. Left: Long-range order (correlation) between any site i and j in the crystal is observed. Right: Only neighboring spins are correlated, and there is no long-range order. This is the first demonstration of such a phase in one-dimensional systems, see Nature 623, 713 (2023).

 

Engineering Floquet Topological Insulator. Top: Interaction matrix between nearest neighbors and next-nearest neighbors spins in a 12-site one-dimensional crystal. Local oscillating Floquet fields (depicted in pink) enable the controllable suppression of odd spin bonds. Bottom: Measured magnetization across the crystal as a function of time for a single spin edge-excitation. In the trivial state (left), excitation thermalizes quickly, but in the Floquet state, thermalization is significantly suppressed. See arXiv:2401.10362 (2024).

 

Another example is a Floquet topological insulator, a spin variant of the SSH model, whose coupling matrix is engineered with side-resolved local oscillating fields. While excitations localized in the bulk thermalize quickly, spin excitations near the edge have longer lifetimes and thermalize more slowly. This unique crystal can host non-trivial fermionic interaction terms and enables the study of topological phases beyond the free-fermionic picture.

The novel techniques discovered and developed in the group provide a new means to explore emerging quantum phases of matter.

Selected Publications

  • “Continuous Symmetry Breaking in a trapped ion spin chain“. Feng, Katz, Haack, Maghrebi, Gorshkov, Gong, Cetina, Monroe. Nature 623, 713-717 (2023).
  • “Observing Topological Insulator Phases with a Programmable Quantum Simulator“, Katz, Feng, Porras, Monroe arXiv:2401.10362 (2024).
  • “Observation of a finite-energy phase transition in a one-dimensional quantum simulator”.Schuckert, Katz, Feng, Crane, De, Hafezi, Gorshkov, Monroe. Nature Physics 21 374-379 (2025).