Impact of pure dephasing on the nonlinear optical response of single quantum dots and dot ensembles

The nonlinear optical response to ultrafast laser pulses of semiconductor quantum dots coupled to acoustic phonons is discussed on the basis of closed-form analytical results valid for dots in the strong confinement regime. General properties of four-wave-mixing (FWM) signals are derived from the analytical formulas. Numerical results are presented for two-pulse FWM signals from single quantum dots and from dot ensembles in the time and the frequency domains. Interestingly, the initial decay time of the signal is found to depend nonmonotonously on temperature and delay time. In general, the phonon coupling leads to a modulated decay of the time domain optical response which is neither exponential nor Gaussian. The strength of the modulations is influenced by inhomogeneous broadening and temperature as well as by the relative localization lengths of electrons and holes. FWM spectra of single dots evolve from asymmetric functions for coinciding pulses into symmetric spectra for large delays. Nonlinear signals are compared with linear signals revealing striking similarities but also significant differences, e.g., concerning the depth of the initial drop.