Two-band density-matrix approach to nonlinear optics of excitons

Abstract

The two-band density-matrix dynamics of a semiconductor driven by an intense light field is set up in a real-space representation. The relation to the corresponding k-space theory is established. The real-space theory is applied to the case of excitonic resonances in a quantum well of finite width. Solutions describing the dynamical Stark effect are studied with particular emphasis on the following points: (i) the dependence of the measured signal on whether the spectral filtering of the probe beam is before or after the sample, and (ii) the influence of short pump pulses, the delay between the pump and the probe pulse, and the dephasing of the pump excitation. A perturbative analytical treatment and a real-time numerical integration of the relevant equations of motion are compared.