Three-dimensional electronic spectroscopy of excitons in asymmetric double quantum wells.

We demonstrate three-dimensional (3D) electronic spectroscopy of excitons in a double quantum well system using a three-dimensional phase retrieval algorithm to obtain the phase information that is lost in the measurement of intensities. By extending the analysis of two-dimensional spectroscopy to three dimensions, contributions from different quantum mechanical pathways can be further separated allowing greater insight into the mechanisms responsible for the observed peaks. By examining different slices of the complete three-dimensional spectrum, not only can the relative amplitudes be determined, but the peak shapes can also be analysed to reveal further details of the interactions with the environment and inhomogeneous broadening. We apply this technique to study the coupling between two coupled quantum wells, 5.7 nm and 8 nm wide, separated by a 4 nm barrier. Coupling between the heavy-hole excitons of each well results in a circular cross-peak indicating no correlation of the inhomogeneous broadening. An additional cross-peak is isolated in the 3D spectrum which is elongated in the diagonal direction indicating correlated inhomogeneous broadening. This is attributed to coupling of the excitons involving the two delocalised light-hole states and the electron state localised on the wide well. The attribution of this peak and the analysis of the peak shapes is supported by numerical simulations of the electron and hole wavefunctions and the three-dimensional spectrum based on a density matrix approach. An additional benefit of extending the phase retrieval algorithm from two to three dimensions is that it becomes substantially more reliable and less susceptible to noise as a result of the more extensive use of a priori information.