Effective magnetic fields for stationary light

We describe a method to create effective gauge potentials for stationary-light polaritons in two or three spatial dimensions. When stationary light is created in the interaction with a uniformly rotating ensemble of coherently driven double $\Lambda$ atoms, the equation of motion is that of a massive Schr\"odinger particle in an effective magnetic field. In addition a repulsive scalar potential emerges which can however be compensated by a space-dependent detuning. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.