Theory of exciton pair states and their nonlinear optical properties in semiconductor quantum dots

The exciton and two-exciton states in semiconductor quantum dots much larger in size than the exciton Bohr radius are investigated, and the energies and oscillator strengths of several exciton and biexciton states are calculated. The presence of weakly correlated exciton-pair states are identified and these have a large oscillator strength increasing proportional to the volume of the quantum dot. These states are shown to play a crucial role in determining the nonlinear optical response of large quantum dots. The weakly correlated exciton-pair states are found to cause a cancellation effect in the third-order nonlinear optical susceptibility at the exciton resonance, providing a consistent understanding of the experimentally observed saturation of the mesoscopic enhancement of the excitonic optical nonlinearity. The excited-state absorption in quantum dots is also studied and the excitation of the weakly correlated exciton-pair states is found to dominate the spectrum. The spectral features in the pump-probe spectroscopy are predicted in detail. The biexciton binding energy and oscillator strength are obtained in good agreement with experimental results on CuCl quantum dots. Also, the good correspondence of the excited-state absorption spectra between the theory and experiments provides convincing evidence for the presence of the weakly correlated exciton-pair states.