In nonlinear optics it is possible to reverse the destructive interference of so-called inhomogeneously broadened systems which contain a distribution of uncoupled subsystems with different resonance frequencies.
For example, consider a four-wave-mixing experiment in which the first short laser pulse excites all transitions at .
As a result of the destructive interference between the different frequencies the overall polarization decays to zero.
A second pulse arriving at  is able to conjugate the phases of the individual microscopic polarizations, i.e., , of the inhomogeneously broadened system.
The subsequent unperturbed dynamical evolution of the polarizations leads to rephasing such that all polarization are in phase at  which results in a measurable macroscopic signal.
Thus, this so-called photon echo occurs since all individual polarizations are in phase and add up constructively at .
Since the rephasing is only possible if the polarizations remain coherent, the loss of coherence can be determined by measuring the decay of the photon echo amplitude with increasing time delay.
When photon echo experiments are performed in semiconductors with exciton resonances, it is essential to include many-body effects in the theoretical analysis since they may qualitatively alter the dynamics. For example, numerical solutions of the SBEs have demonstrated that the dynamical reduction of the band gap which originates from the Coulomb interaction among the photoexcited electrons and holes is able to generate a photon echo even for resonant excitation of a single discrete exciton resonance with a pulse of sufficient intensity.
Besides the rather simple effect of inhomogeneous broadening, spatial fluctuations of the energy, i.e., disorder, which in semiconductor nanostructure may, e.g., arise from imperfection of the interfaces between different materials, can also lead to a decay of the photon echo amplitude with increasing time delay. To consistently treat this phenomenon of disorder induced dephasing the SBEs need to be solved including biexciton correlations.
As shown in Ref. such a microscopic theoretical approach is able to describe disorder induced dephasing in good agreement with experimental results.