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An overview on photon echo spectroscopy under resonant excitation of theexciton complexes in semiconductor nanostructures is presented. The use offour-wave-mixing technique with the pulsed excitation and heterodyne detectionallowed us to measure the coherent response of the system with the picosecondtime resolution. It is shown that, for resonant selective pulsed excitation ofthe localized exciton complexes, the coherent signal is represented by thephoton echoes due to the inhomogeneous broadening of the optical transitions.In case of resonant excitation of the trions or donor-bound excitons, theZeeman splitting of the resident electron ground state levels under the appliedtransverse magnetic field results in quantum beats of photon echo amplitude atthe Larmor precession frequency. Application of magnetic field makes itpossible to transfer coherently the optical excitation into the spin ensembleof the resident electrons and to observe a long-lived photon echo signal. Thedescribed technique can be used as a high-resolution spectroscopy of the energysplittings in the ground state of the system. Next, we consider the Rabioscillations and their damping under excitation with intensive optical pulsesfor the excitons complexes with a different degree of localization. It is shownthat damping of the echo signal with increase of the excitation pulse intensityis strongly manifested for excitons, while on trions and donor-bound excitonsthis effect is substantially weaker.

Photon echo from localized excitons in semiconductor nanostructures