Optical quantum simulation of Abelian gauge field using cold atomic ensembles coupled with arrays of optical cavities

A potentially practical scheme is proposed to realize optical quantum simulation of artificial Abelian gauge field in a scalable architecture consisting of cold atomic ensembles with optical cavities.In the present model,the collective excitations of cold atomic ensembles can be converted to the bosonic modes within the low-excitation limit,where the structure of two-dimension(2D)square plaquette enables the polaritons to move like a charged particle subjected to an external magnetic field.We find that the energy spectrum of this hybrid system exhibits a shape of Hofstadter buttery.Our work provides a different perspective to the quantum simulation of condensed matter and many-body physics in the context of cavity quantum electrodynamics.The experimental feasibility are justified using the existing techniques.