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 magnet
ic 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.
The laser-like coherent emission at 391nm from N$_2$ gas irradiated by strong 800nm pump laser and weak 400nm seed laser is theoretically investigated. Recent experimental observations are well simulated, including temporal profile, optical gain and
periodic modulation of the 391nm signal from N$_2^+$. Our calculation sheds light on the long standing controversy on whether population inversion is indispensable for the optical gain. We demonstrate the Ramsey interference fringes of the emission intensity at 391nm formed by additionally injecting another 800nm pump or 400nm seed, which are well explained by the coherent modulation of transition dipole moment and population between the $A^2Pi_u( u=2)$-$X^2Sigma_g^+$ states as well as the $B^2Sigma_u^+ ( u=0)$-$X^2Sigma_g^+$ states. This study provides versatile possibilities for the coherent control of $text{N}_2^+$ air laser.
