Synthetic Berry curvature in atom-cavity systems

Abstract

In atom-cavity systems, mean field theory is widely used, in which the quantum cavity operator is replaced by a classical amplitude. Then the problem is converted into atoms moving in a self-consistent potential. The mean field treatment captures the physics of cavity mediated interactions, and predicts the self-organized superradiant phase. In this work, however, we show that it fails for certain atom-cavity coupling: it predicts zero ground state atomic current where the fully quantum calculation exhibits a finite one. We find that the origin of this failure is the non-zero Berry curvature in the synthetic dimension spanned by the photon Fock ladder and real space. In this synthetic picture, the atomic current can be understood as Hall response of cavity detuning, whereas mean field collapses this dimension and discards the atom--photon correlations required for its Hall response. The same beyond-mean-field geometry predicts Laughlin-like photon generation under adiabatic flux insertion. Our work identifies synthetic Berry curvature as a concrete mechanism for the breakdown of static mean field in atom--cavity physics.