Towards larger Laughlin states with Rydberg Polaritons*

The rich physics of fractional quantum Hall (FQH) states, including quasi-particle excitations that are neither fermions or bosons, is extremely challenging to controllably explore in condensed matter systems due to limited control at small length scales. However, FQH states are not exclusive to fermions; they can also emerge in strongly interacting bosonic systems under the influence of synthetic gauge fields, as recently demonstrated for photonic and cold atomic two-particle Laughlin states [1-3]. Here, we use a highly degenerate out-of-plane twisted optical cavity combined with a thin atomic cloud of Rubidium atoms to create strongly interacting Rydberg polaritons that effectively live in a two-dimensional manifold. The Rydberg polaritons inherit their strong interactions from their atomic component while simultaneously experiencing dynamics in a synthetic magnetic field through their photonic component dictated by the twisted cavity. We describe our recent progress to enable larger Laughlin states by designing and characterizing a highly degenerate twisted multi-mode cavity. Our platform opens new avenues for exploring displaced and larger Laughlin states. Additionally, we report experimental results on Förster resonance enhanced Rydberg blockade, demonstrating a further step toward scalable synthetic strongly-interacting quantum Hall systems.

[1] Clark, L.W., Schine N., et al. "Observation of Laughlin states made of light". Nature 582, 41-45 (2020)

[2] Léonard, J., Kim, S., et al. “Realization of a fractional quantum Hall state with ultracold atoms”. Nature 619, 495–499 (2023)

[3] Wang, C., Liu, F. “Realization of fractional quantum Hall state with interacting photons”. Science, 384 (2024)