UC Santa Barbara

Quantum mechanics views particles as matter waves rippling through space, and when there are many of these waves present in the same system, they can interfere with one another. While quantum mechanics make the direct measurement of a particular wave function’s phase impossible, clever experiments can probe the interference of wave functions with different phases. High Order Sideband Generation (HSG) is an optical method which uses two frequencies of light to both excite quasiparticle-antiquasiparticle pairs and accelerate them through the Brillouin Zone. In the experiments detailed in this thesis, a near infrared (NIR) laser creates electron-hole (e-h) pairs in bulk Gallium Arsenide (GaAs). A strong Terahertz (THz) electric field ionizes the e-h pair, accelerates the pair to a higher energy, and slams the pair back together to have the e-h pair annihilate and emit a photon. Because the pair will gain energy from the THz acceleration process, the photon emitted by their annihilation will be offset in energy from the initial NIR excitation energy; a high order sideband. While the THz is accelerating the e-h pairs, the holes can be in one of four angular momentum eigenstates which exists in the valence band of bulk GaAs. The distribution of e-h pairs in the four states is determined by the Bloch wave functions and effective Hamiltonian of the valence band, called the Luttinger Hamiltonian. By the conservation of angular momentum, a given hole will produce a sideband with a specific polarization, and the total polarization of sideband photons at a given energy can be related to the Bloch wave functions. The reconstruction of Bloch wave functions in bulk GaAs is detailed in this thesis. The change in polarization as a function of sideband energy is presented as an interferogram. Analogous to a Michelson interferometer for Bloch waves, signal is connected to the difference in dynamical phase accrued by different quasiparticles being accelerated by the THz field. A classical model of the quasiparticle trajectories leads to an analytical theoretical calculation of the sideband polarization, which is in good quantitative agreement with experiment. The sideband polarization dependence on the initial energy of the NIR excitation photons is probed, and preliminary analysis of the dynamical gap of the driven quasiparticles yields a value of Eg = 1.511 eV. In addition, the sideband polarization can be related to the effective Hamiltonian and the dispersion relation of the quasiparticles in bulk GaAs. Beyond the experiments detailed in this thesis, HSG offers the opportunity to characterize the Bloch wave functions, effective Hamiltonians, and dynamical phases of more exotic quasiparticles and more exotic materials. With this thesis acting as a proof-of-concept for the HSG polarimetery methodology, the ambition is to extend this method to highly correlated systems or semiconductors with large spin-orbit coupling, or to measure geometric phases, indicative of non-trivial topologies.