Effective Magnetic Fields for Stationary Light

We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-$\Lambda$ type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. 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 up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.

Figure 1

The Raman interaction of two counterpropagating control lasers of Rabi frequencies ${\Omega }_{\pm }$ and opposite circular polarization coupling to the $|s⟩-|e_{\pm }⟩$ transitions of a double-$\Lambda$ system generates a quasistationary pattern of Stokes fields ${\mathcal{E}}_{\pm }$, called stationary light.