Exciton and biexciton correlations for weakly confined semiconductor quantum wires

The contributions of excitons and biexcitons to the four-wave mixing (FWM) signal are calculated for semiconductor quantum wells with an additional weak wire confinement. In contrast to the giant oscillator model, in our description the biexciton is formed from two singlet excitons by the Coulomb interactions. The matrix elements of the repulsive and attractive interactions between two excitons are calculated explicitly using 2D quantum well wave functions and quantized center-of-mass envelop functions. By calculating the excitonic polarization in the FWM direction, we obtain coherent exciton-biexciton quantum beats as function of the delay between the two pulses and of their intensity. Quantum beat oscillations are found not only on the rising side of the FWM-signal as in spatially homogeneous chi(3)-theories,but also on the falling side, as it is observed experimentally. With increasing intensities the quantum beats develop into irregular signals. (C) 1999 Elsevier Science Ltd. All rights reserved.