It is nowadays possible to generate, in different spectral ranges, ultrabroadband light pulses with transform-limited (TL) duration corresponding to a few optical cycles. Whenever broadband pulses are employed, the dispersion experienced by the pulses causes a frequency chirp which may severely lengthen their duration and influence time-resolved measurements. While it is well known that the relative weight of ground-state versus excited-state oscillations can be controlled by the chirp in the pump pulse, the effects of probe pulse chirp have not been fully investigated. In this paper we show, both theoretically and experimentally, that a pump-probe experiment using strongly-chirped probe pulses can preserve the temporal resolution of the TL pulses.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small
+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small
+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both
+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large
+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small
+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
We present a time-domain treatment of pump–probe experiments with chirped pulses derived from the same laser source. In this theory we treat the nonlinearities as decaying either instantaneously or exponentially. Therefore the results from it cover different mechanisms originating from electronic orbitals, molecular vibrations, molecular orientations, excited-state populations, etc., as long as their decay falls into one of the two classes. We derive expressions for the transmission of the probe in each case. We divide the transmission expression from nonlinearities with exponential decay into a number of terms, each of which describes a unique situation. These include two-beam coupling in the coherent region that is not present with chirp-free pulses, two-photon absorption, and excited-state absorption. We give analytical expressions for the transmission where possible, and we give the first-order approximation and the estimated error when expression in closed form is unattainable. We discuss various aspects of these terms.
We give the first analysis of heterodyne experiments that includes the propagation along the waveguide. Under the assumption that the material polarization is adiabatically eliminated we derive simple analytic expressions for the coherent coupling term, exact for Gaussian pulses and a good approximation for other shapes. We find that the measured signal does not display any phase dependence close to zero pump–probe delay. A four-wave mixing band is identified in the heterodyne signal, and a new class of experiments is proposed by analogy with the spatial case.
Exciton Rabi oscillations and Rabi splitting differ significantly from their atomic counterparts in part because Coulomb interactions between excitons strongly influence the exciton Rabi frequency.' While both exciton Rabi oscillations and Rabi splitting were demonstrated recently in quantum wells (QWs),'.l experimental investigation of how exciton-exciton interactions affect these coherent optical Q~OCCSS~S has been hindered bya number of complications. In time-domain studies, the Rabi frequencyvaries with time due to the changing electric field strength. In typ ical spectral domain studies, a spectrally-broad probe pulse is spectrally resolved after its transmission through the sample. The resulting pump-probe spectra are difficult to interpret due to the presence of coherent spectral oscillations and a sensitive dependence on the pump-probe delay. In this paper we report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field bed theoretical models.' Pump-probe experiments were performed on a 130 A GaAs1AlGa.k multiple QW sample at 10 K. Figure I shows results of pump-probe meas