Transparency, slow light and enhanced nonlinear optics in a four-level scheme

We analyse the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the steady state linear susceptibility of a probe laser field and show that the system can exhibit double electromagnetically induced transparency with controlled group velocity. We also show that a coherently prepared tripod scheme can be used for efficient nonlinear generation of new laser fields.