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Abstract
Can quantum materials be made of light? This exciting possibility requires two primary
ingredients, photons that behave like massive particles and strong interactions between those
photons. This thesis describes our realization of these ingredients and our initial explorations
of the resulting system.
First, we develop a synthetic magnetic eld for harmonically trapped photons and observe
the formation of a Landau level. This enables investigation into three distinct topological
characteristics of a photonic integer quantum Hall system. Next, we turn photons into
strongly-interacting cavity Rydberg polaritons, quasiparticles which inherit their motional
dynamics from the optical cavity and gain strong interactions from Rydberg excitations of a
cold Rubidium gas. Granting these polaritons access to a degenerate Landau level of cavity
states allows them to move, collide, and order themselves into topologically nontrivial material
states. Observations of strong correlations in both real space and angular momentum
space certify the creation and detection of a photonic Laughlin state, a ground state of a fractional
quantum Hall system. Developing synthetic quantum materials out of light provides
fundamentally new experimental capabilities and opportunities and here establishes quantum
many-body optics as a direct route towards breakthroughs in understanding topological
order and strongly correlated materials.