Observation of Pairing in the bosonic Pfaffian Quantum Hall State with ultracold atoms in an Optical Lattice

Topological states of matter, such as fractional quantum Hall states, emerge from the interplay between strong interactions and magnetic fields. Among the most sought-after examples is the Moore–Read (Pfaffian) state, which is predicted to exhibit pairing and nontrivial topological order. Here, we use ultracold Rb 87 atoms in a quantum gas microscope to engineer the 𝜈 = 1 Pfaffian for a system of three particles on a 5×5 lattice. Employing a Bayesian-optimized ramp [1], we prepare the Pfaffian state from a topologically trivial initial state. We directly image hallmark features of the Pfaffian phase, including a central density depletion and pronounced suppression of local three-body correlations relative to a normal state, providing a microscopic signature of pairing. Furthermore, by monitoring the center-of-mass drift of the Pfaffian state under a weak applied force [2], we measure the Hall conductivity, establishing a new probe of fractional quantum Hall physics in few-body atomic systems.

[1]  Blatz, T.  et al. Bayesian optimization for robust state preparation in quantum many-body systems, Quantum 8, 1388 (2024). https://doi.org/10.22331/q-2024-06-27-1388

[2] Repellin, C., Léonard, J., and Goldman N. Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles.” Physical Review A, vol. 102, no. 6 (2020). https://doi.org/10.1103/PhysRevA.102.063316