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

Abstract

While time-resolved pump-probe differential reflectivity and transmitivity measurements are routinely used to monitor the population relaxation dynamics on the subpicosecond time scale, it is also known that the signal in the negative delay can yield direct signatures of the perturbed-free-induction-decay of polarization. Yet this technique, especially in reflection geometry, has never been popular because the experiment is conceptually not very intuitive. Coherent dynamics is therefore usually studied using the more complex four-wave-mixing experiments. Here we derive from first principles the simplest possible but mathematically complete framework for the negative delay signal in both the time and the spectral domains. 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 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, although exact fitting of the experimental spectra with the theoretical expression is difficult. This is on account of additional resonances present in the sample corresponding to lower energy bound states.