Quantum beats are observable in systems in which the total optical polarization is due to a finite number of discrete transition frequencies which are quantum mechanically coupled, e.g., by common ground or excited states.
Assuming for simplicity that all these transitions have the same dipole matrix element, after excitation with a short laser pulse at  the optical polarization  of the system evolves as
where the index  labels the participating transitions.
A finite number of frequencies results in temporal modulations of the squared modulus of the polarization  and thus of the intensity of the emitted electromagnetic field  with time periods
For the case of just two frequencies the squared modulus of the polarization is proportional to
i.e., due to the interference of two contributions with the same amplitude but different frequencies, the polarization varies between a maximum and zero.
In semiconductors and semiconductor heterostructures, such as quantum wells, nonlinear optical quantum-beat spectroscopy has been widely used to investigate the temporal dynamics of excitonic resonances.
In particular, the consequences of many-body effects which depending on the excitation conditions may lead to, e.g., a coupling among different excitonic resonances via biexcitons and other Coulomb correlation contributions and to a decay of the coherent dynamics by scattering and dephasing processes, has been explored in many pump-probe and four-wave-mixing measurements.
The theoretical analysis of such experiments in semiconductors requires a treatment on the basis of quantum mechanical many-body theory as is provided by the SBEs with many-body correlations incorporated on an adequate level.