Advent of ultrashort lasers made it possible to probe various scattering phenomena in materials that occur in a time scale on the order of few femtoseconds to several tens of picoseconds. Nonlinear optical spectroscopy techniques, such as pump-probe, transient four wave mixing (TFWM), etc., are very common to study the carrier dynamics in various material systems. In time domain, the transient FWM uses several ultrashort pulses separated by time delays to obtain the information of dephasing and population relaxation times, which are very important parameters that govern the carrier dynamics of materials. A recently developed multidimensional nonlinear optical spectroscopy is an enhanced version of TFWM which keeps track of two time delays simultaneously and correlate them in the frequency domain with the aid of Fourier transform in a two dimensional map. Using this technique, the nonlinear complex signal field is characterized both in amplitude and phase. Furthermore, this technique allows us to identify the coupling between resonances which are rather difficult to interpret from time domain measurements. This work focuses on the study of the coherent response of a two dimensional electron gas formed in a modulation doped GaAs/AlGaAs quantum well both at zero and at high magnetic fields. In modulation doped quantum wells, the excitons are formed as a result of the inter- actions of the charged holes with the electrons at the Fermi edge in the conduction band, leading to the formation of Mahan excitons, which is also referred to as Fermi edge singularity (FES). Polarization and temperature dependent rephasing 2DFT spectra in combination with TI-FWM measurements, provides insight into the dephasing mechanism of the heavy hole (HH) Mahan exciton. In addition to that strong quantum coherence between the HH and LH Mahan excitons is observed, which is rather surprising at this high doping concentration. The binding energy of Mahan excitons is expected to be greatly reduced and any quantum coherence be destroyed as a result of the screening and electron-electron interactions. Such correlations are revealed by the dominating cross-diagonal peaks in both one-quantum and two-quantum 2DFT spectra. Theoretical simulations based on the optical Bloch Equations (OBE) where many-body effects are included phenomenologically, corroborate the experimental results. Time-dependent density functional theory (TD-DFT) calculations provide insight into the underlying physics and attribute the observed strong quantum coherence to a significantly reduced screening length and collective excitations of the many-electron system. Furthermore, in semiconductors under the application of magnetic field, the energy states in conduction and valence bands become quantized and Landau levels are formed. We observe optical excitation originating from different Landau levels in the absorption spectra in an undoped and a modulation doped quantum wells. 2DFT measurements in magnetic field up to 25 Tesla have been performed and the spectra reveal distinct difference in the line shapes in the two samples. In addition, strong coherent coupling between landau levels is observed in the undoped sample. In order to gain deeper understanding of the observations, the experimental results are further supported with TD-DFT calculation.

We correlated experimental results with theoretical estimations of the dielectric function ε(ω) in two contexts: the effect of an electric field in quantum wells and that of the spin polarization of an interacting electron-hole plasma in bulk semiconductors. In the first part, we recorded photoreflectance spectra from Ge/GeSi quantum wells of different widths but having comparable builtin electric fields caused by doping. The reason why the spectra differed in overall shape was difficult to understand by conventional methods, for example, by calculating the allowed transition energies or by fitting the data with lineshape functions at each transition energy. Instead, we computed the photoreflectance spectra from first-principles by using the confined electron and hole wavefunctions. This method showed that the spectra differ in overall shape because of the experimentally hitherto unobserved trend in quantum well electro-optical properties, from the quantum confined Franz-Keldysh effect to the bulk Franz-Keldysh effect, as the well width is increased. The second part develops a threeband microscopic theory for the optical properties due to spin-polarized carriers in quasiequilibrium. We show that calculations based on this theory reproduce all the trends observed in a recent circularly polarized pump-probe experiment reported in the literature. To make the computation less intensive, we proposed a simplified, two-band version of this theory which captured the main experimental features. Besides, we constructed a cw diode laser-based pump-probe setup for our own optical studies of spin-polarized carriers by Kerr rotation. We achieved a sensitivity of detection of Kerr rotation of 3 x 10¯ 8 rad, corresponding to an order of magnitude improvement over the best reports in the literature. The efficacy of our setup allowed for the demonstration of a pumpinduced spin polarization in bulk GaAs, under the unfavorable conditions of steady-state and room temperature.