High Efficiency Four-Wave Mixing with Relaxation Coupling of Longitude-Optical Phonons in Semiconductor Quantum Wells* *Supported by Program for Changjiang Scholars and Innovative Research Team in University under Grant (IRT1080), National Natural Science Foundation of China under Grant Nos. 51272158, 11374252, and 51372214, Changjiang Scholar Incentive Program under Grant No. [2009] 17, Scientific Research Fund of Hunan Provincial Education Department of

Abstract

The time-dependent analysis of four-wave mixing (FWM) has been performed in four-level double semiconductor quantum wells (SQWs) considering the cross-coupling of the longitude-optical phonons (LOP) relaxation. It is shown that both the amplitude and the conversion efficiency of the FWM field enhance greatly with the increasing strength of cross-coupling of LOP relaxation. Interestingly, a double peak value of the conversion efficiency is obtained under a relatively weak single-photon detuning considering the LOP coupling. When the detuning becomes stronger, the double peaks turn into one peak appearing at the line respect to the about equality two control fields. The results can be interpreted by the effect of electromagnetically induced transparency and the indirect transition. Such controlled high efficiency FWM based on the cross-coupling LOP may have potential applications in quantum control and communications.