Two-Dimensional Fourier-Transform-Spectroscopy (2DFTS) is a novel method for the experimental investigation of many-body interactions in semiconductor nanostructures [1]. It displays directly the heavy-hole (hh) and light-hole (lh) excitonic transitions in III-V-quantum wells along the main diagonal of a two-dimensional plot which is spanned by the excitation energy -hω{sub}τ and the emission energy hω{sub}t. In addition, characteristic signatures due to continuum excitations appear as well as mixed peaks in off-diagonal positions resulting from various couplings. Using a one-dimensional tight-binding model which contains the correct selection rules we compute 2DFTS in the coherent χ{sup}(3)-limit. By comparing theoretical spectra resulting from different orders in the Coulomb interaction we can clearly identify the influence of the many-particle interaction on the various signatures that are visible in the spectrograms. The distribution of the peak heights, their magnitude, and their line-shape are of particular interest. Co-circularly polarized excitation pulses are considered. Figure 1d shows the result taking into account only the Pauli-blocking nonlinearity. The upper diagonal peak corresponds to the hh- and the lower one to the lh-excitonic resonance. The structure along the diagonal is due to the continuum, which in this calculation appears as a succession of peaks due to the finite energy resolution in our calculations. The fact that the continuum appears at the diagonal confirms that in this limit it is partly represented by an ensemble of uncoupled two-level systems. However, the vertical signatures confirm the coupling of the continuum to the exciton by the Pauli-nonlinearity. In the Hartree-Fock results, Fig. 1c, the continuum peaks along the diagonal vanish, i.e., the ensemble of uncoupled two-level systems becomes completely inadequate. Due to the fact that for the chosen co-circular polarization the hh- and lh-excitonic resonances belong to optically uncoupled subspaces there are no mixed excitonic peaks in off-diagonal positions within Hartree-Fock. Including the many-body correlations, Fig. 1b, leads to significant changes of the excitonic resonances on the diagonal and the appearance of their mixed contributions at non-diagonal positions. E.g., the mixed excitonic peak below the diagonal is a pure correlation contribution. The upper non-diagonal peak is suppressed due to small overlap with the excitation pulse spectrum together with the smaller dipole matrix element of the lh-exciton. It is also evident that there are strong couplings between the excitons and the continuum due to correlations, as evidenced by the enhanced vertical continuum features. The peak distribution and their lineshape show a good agreement with the experiment Fig. 1a. This demonstrates that this method is able to provide a wide spectrum of information about Coulomb-induced couplings in various systems. In particular, the measurement of real and imaginary parts gives additional phase-dependent information and biexcitonic contributions can be studied by analyzing at the polarization dependence of the spectra [2].
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