Excitonic wave packets in ${\mathrm{In}}_{0.135}$ ${\mathrm{Ga}}_{0.865}$ As/GaAs quantum wires

We have investigated the coherent dynamics of excitonic wave packets in ${\mathrm{In}}_{0.135}$ ${\mathrm{Ga}}_{0.865}$ As/GaAs quantum wires with lateral widths between 29 and 85 nm by means of time-integrated degenerate four-wave mixing. In the decay of the coherent polarization, we observe periodic modulations, which we ascribe to quantum beats between the ground state and the first excited state of the heavy-hole exciton in the quantum wires. The period of these beats decreases with decreasing wire width, indicating an increase of the exciton binding energy due to lateral quantization. The experimentally observed binding energy rises from 8.7 meV for the two-dimensional reference, up to 11.7 meV for the 29-nm-wide quantum wires. Detailed calculations of the exciton binding energy for these structures are in agreement with the experimental data.