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

We present a theoretical study of a rotating trapped photon gas where a Laguerre-Gauss laser pump with a non-zero orbital angular momentum is used to inject rotating photons into a cavity with strong optical nonlinearity. 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 quantum Hall liquid of photons 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.