  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.
