Rydberg atom arrays as programmable quantum matter

6 problems

• Universality class of the $Z3$ ordering transition in Rydberg chains

  Contested

  Rydberg chains can order with one excitation every third atom. The transition into this order may belong to an unusual chiral class or pass through an intermediate floating phase.

• Liquid, glass or crystal in blockaded Rydberg atoms on a kagome lattice

  Contested

  Atoms on a kagome lattice (corner-sharing triangles) that block their neighbours from being excited showed, in early calculations, a disordered region that might be a quantum spin liquid. Later calculations found glassy behaviour or no liquid at all.

• Is the kagome dipolar XY Rydberg magnet a Dirac spin liquid?

  Open

  Rydberg atoms can swap excitations with their neighbours, which makes a magnet with competing interactions on a kagome lattice. Calculations predict a spin liquid with massless particle-like excitations, and a 2026 experiment reported a candidate.

• Is the Rydberg ruby-lattice spin liquid an equilibrium ground state?

  Contested

  A 2021 experiment saw signs of a quantum spin liquid, a state with hidden long-range quantum entanglement, in atoms on a ruby-shaped lattice. It is unclear whether this was a true lowest-energy state or a product of fast driving.

• Nature of the striated and star transitions in square Rydberg arrays

  Open

  On a square grid, Rydberg atoms form several ordered patterns. The transitions into some of them may be smooth or abrupt, and this is not settled.

• String-breaking rates in Rydberg lattice gauge theories

  Partially resolved

  A string of field between two charges can snap by creating a new pair of particles, as in the binding of quarks. Rydberg arrays have shown this snapping, and the task is to measure how fast it happens.