Paper detail

Phase-dependent double-Λ electromagnetically induced transparency

We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ 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-Λ EIT scheme.