Transient interband light absorption by quantum dots: Nondegenerate case of pump-probe spectroscopy

A theoretical description of the pump-probe optical method is presented that is adapted to semi-conductor quantum dots and makes it possible to determine the energy relaxation rates of the excited states of electron-hole pairs and excitons in these objects. A scheme of the method is considered in which the carrier frequencies of optical pump and probe pulses are close to the resonance with different interband transitions of the quantum-dot electron subsystem (nondegenerate case). It is assumed that the final states to which electron subsystem passes as a result of the absorption of pump and probe pulses are interrelated by intraband relaxation. The probe-pulse energy absorption induced by the pump pulse is analyzed as a function of the delay time between the pulses. It is shown that this dependence tends to be biexponential under certain conditions. The exponential factors are proportional to the energy relaxation rates of the resonantly excited states of electron-hole pairs and excitons, while the preexponential factors depend on the intraband relaxation rate.