How pump–probe differential reflectivity at negative delay yields the perturbed-free-induction-decay: theory of the experiment and its verification

Abstract

We present a simple but mathematically complete first-principles theory for the pump–probe differential reflectivity experiment at negative delay (probe preceding the pump) to show how it gives information about the perturbed-free-induction-decay of coherent polarization. The calculation, involving the optical Bloch equations to describe the induced polarization and the Ewald–Oseen idea to calculate the reflected signal as a consequence of the free oscillations of perturbed dipoles, also explicitly includes the process of lock-in detection of a double-chopped signal after it has passed through a monochromator. The theory giving a closed form expression for the measured signal in both time and spectal domains is compared with experiments on high quality GaAs quantum well sample. The dephasing time inferred experimentally at 4 K compares remarkably well with the inverse of the absorption linewidth of the continuous-wave photoluminescence excitation spectrum. Spectrally-resolved signal at negative delay calculated from our theoretical expression nicely reproduces the coherent spectral oscillations observed in our experiments, although exact fitting of the experimental spectra with the theoretical expression is difficult on account of multiple resonances.