  The quest of utilizing neutral particles to simulate the behaviour of charged
particles in a magnetic field makes the generation of artificial magnetic field
of great interest. The previous and the only proposal for the production of
synthetic magnetic field for the dark state polaritons in electromagnetically
induced transparency invokes the mechanical rotation of a sample. Here, we put
forward an optical scheme to generate effective gauge potentials for
stationary-light polaritons. 5To demonstrate the capabilities of our approach,
we present recipes for having dark state polaritons in degenerate Landau levels
and in driven quantum harmonic oscillator. Our scheme paves a novel way towards
the investigation of the bosonic analogue of the fractional quantum Hall effect
by electromagnetically induced transparency.
