χ(3)formalism in optically excited semiconductors and its applications in four-wave-mixing spectroscopy

The truncation of the infinite hierarchy of equations of motion is discussed for optically excited semiconductors. We derive a complete set of equations of motion, which are valid up to third order in the excitation field amplitude. To illustrate the results the induced four-wave-mixing signals for linearly polarized laser fields are computed by numerically integrating the ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ semiconductor Bloch equations. As the dominating nonlinearity, a strong excitation-induced dephasing effect is obtained in the ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ regime.