Preprint describes three-particle bosonic Pfaffian state in ultracold rubidium atoms

A team led by researchers in physicist Markus Greiner’s ultracold-atom program has posted a preprint reporting a three-particle bosonic Pfaffian quantum Hall state in ultracold atoms, a closely watched class of states because of their connection to non-Abelian topological order. The paper, posted June 10 to arXiv as 2606.12409v1, describes a minimal experimental realization in rubidium-87 atoms — not a demonstration of braiding, non-Abelian exchange statistics or a usable topological qubit.

That distinction matters. Pfaffian states, also known as Moore-Read states, are important in quantum physics because in larger many-particle systems they are predicted to host exotic excitations whose exchange depends on order, a defining feature of non-Abelian behavior. Those properties have made them relevant to proposals for topologically protected quantum information processing. But the new report is a three-particle experiment, not evidence that a full many-body topological phase has been built or controlled.

The preprint, “A Pfaffian quantum Hall state of ultracold bosons,” lists Joyce Kwan and Greiner among 10 authors, with Kwan as the arXiv submitter. In the abstract, the authors write: “Here we realize a three-particle bosonic Pfaffian state of ultracold 87Rb atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field.”

According to the paper abstract and assignment details, the team used ultracold rubidium-87 atoms trapped in an optical lattice, a grid of light that can hold atoms in place, while engineering an artificial magnetic field through periodic driving. They say the state was prepared with a Bayesian-optimized adiabatic protocol, meaning a step-by-step tuning sequence refined by an optimization method.

The main evidence comes from two kinds of measurements. First, the authors report site-resolved multipoint density correlations, a technique that can track how atoms are distributed across the lattice one site at a time. In the abstract, they say these measurements show “pronounced suppression of short-range three-body coincidences,” a signature they interpret as consistent with the Pfaffian state’s pairing structure. Second, they report Hall-drift measurements aimed at probing the state’s transport response, another standard way to test whether a system behaves like a quantum Hall state.

The Pfaffian state has a long history in theory. Introduced in 1991 by Gregory Moore and Nicholas Read, the Moore-Read or Pfaffian state is a paired fractional quantum Hall state, distinct from the better-known Laughlin family of states. Electronic systems, especially those connected to the 5/2 fractional quantum Hall effect, have long been studied as possible Pfaffian platforms. Ultracold atoms are attractive because they offer unusual control over the system and allow site-resolved measurements alongside engineered gauge fields.

The new preprint also fits into a recent line of work from the Greiner group. In 2023, the group reported a minimal Laughlin-type fractional quantum Hall state with ultracold atoms in a Nature paper. The new result, if it holds up, would move that program from Laughlin-type physics to a Pfaffian pairing state, a qualitatively different target.

Still, the paper’s scope is narrow, and it remains a preprint. As of June 11, no peer-reviewed journal publication for this manuscript was identified in the research report underlying this assignment. The authors themselves frame the work as an early step rather than a final demonstration, writing in the abstract that the measurements “lay the groundwork for future explorations of anyonic braiding.”

For now, the significance is not that non-Abelian anyons have been directly observed or manipulated, but that an experimental platform designed for that broader goal says it has reached a minimal Pfaffian-state milestone in a highly controlled cold-atom setting.