We study a combination of a four-level electromagnetically induced transparency and second-order nonlinearity, and show that the efficiency of frequency conversion can be profoundly enhanced in an erbium-doped glass.
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.
In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.