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We propose that an artificial electromagnetic field can be engineered in thecontext of cold fermionic atoms that are coupled to a cavity mode viatwo-photon processes in a two-dimensional optical lattice. There is astanding-wave pump laser inducing the electric effect in one spatial direction,and a second running-wave laser beam generates the magnetic flux perpendicularto the lattice plane. In the static scenario, the bulk spectrum resembles thefractal structure of the Hofstadter butterfly and the edge mode spectrumindicates the occurrence of the quantum Hall phase. The Keldysh formulism isutilized to capture the time evolution. The back action between atoms andcavity field gives a picture of the time-dependent non-equilibrium dynamics. Wefind that the spontaneous emergence of the artificial electromagnetic fieldstimulates the Hall current, and the superradiant cavity field emerges withoutpump threshold. Moreover, the magnetic flux not only modify the bulk topology,but also drives a series of dynamical phase transitions.

Artificial electromagnetic field with cold atoms in two-dimensional optical lattice