This dissertation covers two projects that were in the logical path to studying decoherence in a high mobility GaAs two--dimensional electron gas at high magnetic fields. The first project is the ultrafast non--degenerate pump--probe spectroscopic study of bulk GaAs in the Split Florida Helix at the National High Magnetic Field Laboratory at Florida State University. This project was undertaken as a proof of concept that ultrafast optics could be done in the Split Florida Helix so that we might study a high mobility two dimensional electron gas using THz time--domain spectroscopy at high magnetic fields, which is a much more complicated measurement than the pump--probe discussed here. This demonstration was a success. We completed the first ultrafast optical study of any kind in the Florida Split Helix. We collected differential reflection data from this bulk sample that exhibited electronic and oscillatory components. These components were treated independently in the analysis by treating the electronic dynamics with a four level approximation. The electronic transition rates were extracted and agreed well with published values. This agreement is a demonstration that the spectrometer functioned as desired. The oscillatory response was found to be a result of the emission of coherent phonons upon electronic transition between the four levels. The frequency of the oscillatory response was extracted and agreed well with the theoretical value.;The second project is the study of the temperature dependence of the cyclotron decay lifetimes in a Landau quantized GaAs high mobility two dimensional electron gas using THz time--domain spectroscopy at relatively low magnetic field (1.25 T). We find that the cyclotron decay lifetimes decrease monotonically with increasing temperature from 0.4 K to 100 K and that the primary pulse amplitudes increase from 0.4 K to 1.2 K, saturates above 1.2 K up to 50 K, and decreases rapidly above 50 K. We attribute this rapid drop in amplitude above 50 K as well as the high temperature behavior of the cyclotron resonance decay times to polar optical phonon scattering. We find that the dissipative component of the measured cyclotron decay lifetimes can not be well approximated by a DC scattering lifetime model, which includes polar optical phonon scattering, remote ionized impurity scattering, acoustic deformation potential scattering, and piezo--electric scattering. This discrepancy is due to the entirely different distribution of the Fermi surface resulting from the Landau quantization of the quantum well's states. This project demonstrates the type of measurements we would like to conduct at higher magnetic fields using more broadband THz sources.;Future work is finally discussed, which outlines the construction and demon- stration of a custom ultra broadband THz time--domain spectrometer for use in the Florida Split Helix. The data collected is not of sufficient quality to extract physical meaning due to its decreased signal to noise and bandwidth relative to the test of the system through the magnet without sample or windows at 0 T and 300 K, which demonstrated the generation and detection of 15 THz of usable bandwidth. This reduction in signal to noise and bandwidth is due to clipping the THz beam on the magnet aperture. Future measurements will use optically clear windows that are also transparent in the THz so that alignment of the THz beam may be done with an optical beam. While the original goal was an extension of the temperature dependent measurements described in the previous paragraph at much higher applied magnetic field strength, the design, construction, and demonstration of the system without sample or windows as well as the data set collected through a high mobility GaAs two dimensional electron gas at 25 T and 15 K constitutes the first THz time--domain measurements conducted in the Florida Split Helix.
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