Exploring Magneto-Excitons in Bulk and Mono-Layer Semiconductors Using Non-Linear Spectroscopy Techniques

The research in two-dimensional (2D) materials has evolved from ``traditional quantum wells based on group III-V and II-VI semiconductors to atomically thin sheets of van der Waals materials such as 2D semiconducting Transition Metal Dichalcogenides (TMDs). These 2D materials remain a stimulating field that continues to introduce new challenges. From both a fundamental physics and technological perspective, magneto-optical spectroscopy has been an essential tool in this research field. TMDs, for example, pose the challenge of characterizing their spin-valley-resolved physics and deriving implications in quantum computation and information research. With the discovery of valley Zeeman effects, the spin-valley physics of TMDs have become profoundly understood by utilizing various magneto-optical spectroscopy techniques. Also, magneto-optical studies may be able to resolve some of the remaining problems in well-understood systems like Gallium Arsenide (GaAs). In this context, using magneto-optical nonlinear spectroscopy, we explore exciton dynamics of bulk and monolayer semiconductor materials under applied magnetic fields. To study the nonlinear response optically, we deploy the Transient Four-Wave Mixing (TFWM) technique. The TFWM technique measures the dephasing and population relaxation in the time domain by using a configuration of several ultra-short pulses separated by time delays. Recent advancements of the multidimensional nonlinear spectrometer (MONSTR) provide the four beams with coordinated time delays. When two-time delays are tracked simultaneously and correlated in the frequency domain with the aid of Fourier transform, it can generate a 2D map. The described technique provides the analysis of complex nonlinear signals for amplitude and phase. Furthermore, the coherent coupling between the states can be isolated as well as inhomogeneous linewidth of the coherence can be estimated using this technique. In this study, two variants of TFWM are used: Two-Dimensional Fourier Transform Spectroscopy (2DFTS) and Time Integrated Four-Wave Mixing (TI-FWM). The main objective of this thesis is to study exciton dynamics using nonlinear spectroscopy under the influence of an external magnetic field. In bulk GaAs, the band structure has distinct characteristics that give rise to the splitting of different excitonic states when external magnetic fields are applied. The splitting of the conduction and valance bands gives rise to different Zeeman components according to their allowed optical selection rules. When studying these effects using 2DFTS, the Zeeman components appear as a distinguishable feature in 2D spectra. Thus, the contribution from coherent coupling as well as proper identification of each Zeeman components can be possible. While two quantum spectra were acquired to investigate higher four-particle correlation at higher magnetic fields, which reveals the role of Zeeman splitting into two quantum transitions. The experimental two-dimensional spectra are reproduced using optical Bloch equations, and many-body effects are included phenomenologically. The second material used in this study is a monolayer of ${\mathrm{WSe}}_{2}$; studying this new class of 2D material under a magnetic field provides a deep understanding of how the excitation dynamics alter under applied magnetic field at the monolayer regime. The dynamics of bright and dark excitons under the high magnetic field can be explored using polarization-dependent TI-FWM measurements. When the magnetic field up to 25 Tesla is applied parallel to the ${\mathrm{WSe}}_{2}$ plane, there is a partial brightening of the energetically lower-lying exciton, which increases the dephasing time. The simultaneous excitation of the bright and dark states results in coherent quantum beating between the two states, which can be observed in TI-FWM spectra. While magnetic fields perpendicular to the sample plane causes hybridization of states due to mutual energy level shift in the bight and dark states at the K and K’ valleys. The hybridization of the states also prolongs the dephasing time. Time-dependent density function theory calculations well reproduce our experimental results. According to these results, magnetic fields can be used to control both the dephasing and coupling of optical excitations in atomically thin semiconductors. Measurement and control of coherent excitations in two-dimensional materials are vital for quantum applications, including quantum computing and quantum information