Electromagnetically-induced-transparency-enhanced Kerr nonlinearity: Beyond steady-state treatment

A time-dependent perturbation calculation for a four-level system is presented. A resonantly enhanced Kerr nonlinearity is produced with a combination of long, short, and delayed laser pulses in the presence of electromagnetically induced transparency. We show the enhanced Kerr nonlinearity and vanishingly small linear susceptibility due to the induced transparency, both are favorable for cross-phase modulation. In addition, we show that possible constructive and destructive interference between different excitation pathways could also lead to enhancement and suppression of the Kerr nonlinearity.