Enhanced Kerr nonlinearity for self-action via atomic coherence in a   four-level atomic system
  Enhancement of optical Kerr nonlinearity for self-action by electro-magnetically induced transparency in a four-level atomic system including dephasing between the ground states is studied in detail by solving the density matrix equations for the atomic levels. We discern three major contributions, from energy shifts of the ground states induced by the probe light, to the third-order susceptibility in the four-level system. In this four-level system with the frequency-degenerate probes, quantum interference amongst the three contributions can, not only enhance the third-order susceptibility more effectively than in the three-level system with the same characteristic parameters, but also make the ratio between its real and imaginary part controllable. Due to dephasing between the two ground states and constructive quantum interference, the most effective enhancement generally occurs at an offset that is determined by the atomic transition frequency difference and the coupling Rabi frequency. 
Tao Hong, Michael Wong Jack, Makoto Yamashita and Takaaki Mukai