We theoretically investigate a double-{Lambda} electromagnetically induced transparency (EIT) system. The property of the double-{Lambda} medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-de
pendent mechanism differentiates the double-{Lambda} medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Maxwell-Bloch equations. In addition, we discuss efficient all-optical phase modulation and coherent light amplification based on the proposed double-{Lambda} EIT scheme.
We observed electromagnetically-induced-transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of 3.8(9)% was observed in a four-level system of cold 87Rb atoms using a driving laser pulse wi
th a peak intensity of approximately 80 {mu}W/cm^2, corresponding to an energy of approximately 60 photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of 46(2)% was demonstrated when applying this scheme using a driving laser intensity of approximately 1.8 mW/cm^2. According to our theoretical predictions, this FWM scheme can achieve a conversion efficiency of nearly 100% when using a dense medium with an optical depth of 500.
