Perturbative solution for analysis of coherent processes in a double-Λ atomic scheme

Abstract

We solve optical Bloch equations (OBEs) for the atomic scheme that consists of four atomic levels which constitute double-lambda (DΛ) configuration i.e. two Λ systems sharing the same two ground levels. DΛ atomic scheme has being used as a basis for many interesting applications in atomic physics and nonlinear optics. It was studied in the context of electromagnetically induced transparency (EIT) Shpaisman et al. (2005) [1], four-wave mixing Baolong et al. (1998) [2], lasers without inversion Kocharovskaya et al. (1990) [3], etc. More recently, efficient application of DΛ scheme led to the development of phenomena like slow and stored light Eilam et al. (2008) [4], quantum mechanical entanglement of two beams of light Boyer et al. (2008) [5] and squeezed light Imad et al. (2011) [6].Typically, a numerical solution of OBEs is used in the theoretical treatment of atomic system of two Λ schemes. In this work, interactions of four laser fields driving a DΛ level scheme were analyzed by using perturbative method to solve OBEs Dimitrijević et al. (2011) [7]. Perturbative method produces simpler solutions such that analytical expressions can be obtained. The comparison of results obtained using lower-order corrections of perturbative method, and the exact calculations using optical Bloch equations is presented. Analytical expressions provide valuable information about processes that occur in the DΛ atomic system. These informations cannot be deduced from the numerical solutions of the OBEs for the same atomic scheme.