Optical properties of excitons in GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As symmetric double quantum wells

Molecular-beam-epitaxy-manufactured GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As symmetric coupled-double-quantum-well (CDQW) structures covering a wide range of coupling strengths have been studied by photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy. These measurements give exciton energy levels and relative absorption strengths of exciton resonances in CDQW’s. In CDQW’s, the electronic states related to one-particle states in the corresponding single quantum wells split into symmetric and antisymmetric states. The exciton states constructed from products of either symmetric or antisymmetric hole and electron one-particle states are denoted ‘‘symmetric’’ and ‘‘antisymmetric’’ excitons. An important feature in the experimental PLE spectra is a significant reduction of oscillator strengths for optical transitions related to antisymmetric heavy-hole and light-hole excitons compared to the strengths of the transitions to the symmetric exciton states when the symmetry splitting becomes comparable to single-quantum-well exciton binding energies. This effect is absent in the simplest theory for CDQW’s, but it can be obtained within an improved effective-mass theory. The Coulomb interaction between electrons and holes mixes symmetric exciton states with antisymmetric exciton states. We have performed variational calculations of exciton binding energies and oscillator strengths for optical transitions to excitonic states which are linear combinations of symmetric and antisymmetric exciton states. The energy levels obtained from the model with mixing between the states are in reasonable agreement with experimental results. However, the difference between the theoretical results with mixing and without mixing is too small to show that the mixing of the states is important. The experimental values for the ratios of oscillator strengths show a decreasing trend with reduced coupling between the wells, as anticipated from the theoretical results with mixing of exciton states. This demonstrates that mixing of exciton states by the Coulomb interaction is important for weakly coupled wells.