  We propose that an artificial electromagnetic field can be engineered in the
context of cold fermionic atoms that are coupled to a cavity mode via
two-photon processes in a two-dimensional optical lattice. There is a
standing-wave pump laser inducing the electric effect in one spatial direction,
and a second running-wave laser beam generates the magnetic flux perpendicular
to the lattice plane. In the static scenario, the bulk spectrum resembles the
fractal structure of the Hofstadter butterfly and the edge mode spectrum
indicates the occurrence of the quantum Hall phase. The Keldysh formulism is
utilized to capture the time evolution. The back action between atoms and
cavity field gives a picture of the time-dependent non-equilibrium dynamics. We
find that the spontaneous emergence of the artificial electromagnetic field
stimulates the Hall current, and the superradiant cavity field emerges without
pump threshold. Moreover, the magnetic flux not only modify the bulk topology,
but also drives a series of dynamical phase transitions.
