Many-body braiding phases in a rotating strongly correlated photon gas

We present a theoretical study of fractional quantum Hall physics in a rotating gas of strongly interacting photons in a single cavity with a large optical nonlinearity. Photons are injected into the cavity by a Laguerre-Gauss laser beam with a non-zero orbital angular momentum. The Laughlin-like few-photon eigenstates appear as sharp resonances in the transmission spectra. Using additional localized repulsive potentials, quasi-holes can be created in the photon gas and then braided around in space: an unambiguous signature of the many-body Berry phase under exchange of two quasi-holes is observed as a spectral shift of the corresponding transmission resonance.