Steady-state linear optical properties and Kerr nonlinear optical response of a four-level quantum dot with phonon-assisted transition

The linear optical properties and Kerr nonlinear optical response in a four-level loop configuration GaAs/AlGaAs semiconductor quantum dot are analytically studied with the phonon-assisted transition (PAT). It is shown that the changes among a single electromagnetically induced transparency (EIT) window, a double EIT window and the amplification of the probe field in the absorption curves can be controlled by varying the strength of PAT κ. Meanwhile, double switching from the anomalous dispersion regime to the normal dispersion regime can likely be achieved by increasing the Rabi energy of the external optical control field. Furthermore, we demonstrate that the group velocity of the probe field can be practically regulated by varying the PAT and the intensity of the optical control field. In the nonlinear case, it is shown that the large SPM and XPM can be achieved as linear absorption vanishes simultaneously, and the PAT can suppress both third-order self-Kerr and the cross-Kerr nonlinear effect of the QD. Our study is much more practical than its atomic counterpart due to its flexible design and the controllable interference strength, and may provide some new possibilities for technological applications. (paper)