Bakr, Waseem SHasan, Areeq2024-07-032026-09-292024-07-032026-09-292024-04-152024-07-03http://arks.princeton.edu/ark:/88435/dsp01ff365858whttps://theses-dissertations.princeton.edu/handle/88435/dsp01ff365858wSpectroscopic techniques have been widely used to study continuum strongly correlated cold atom systems. Examples include measurement of superfluid pairing gaps, quasiparticle dispersions and polaron binding energies in a Fermi gas near a Feshbach resonance [8,12,14,15,17,18,21]. On the other hand, spectroscopy has been much less utilized in the context of Hubbard systems [1] due to the smaller energy scales in optical lattices, which imposes a challenge in terms of the required energy resolution. In recent years, magnetic polarons in doped Fermi-Hubbard systems have received much attention by the cold atom community because of the important role they play in understanding the complex many-body states that emerge in many materials, ranging from the cuprate high-temperature superconductors to moire materials. Nevertheless, experiments have been restricted to detecting polaron signatures through imaging spin and density correlations [6,7,13]. In this thesis, we experimentally develop the technique of Raman spectroscopy of Fermi-Hubbard systems, theoretically proposed by Morera et al. [11]. We study various linewidth broadening mechanisms including magnetic field fluctuations, excited state scattering, noise introduced by propagation through optical fibers, fluctuating differential Stark shifts and harmonic trapping. After addressing these challenges, we are able to obtain a frequency resolution well below the tunneling matrix element in the lattice. As an application of this technique, we spectroscopically detect magnons in the square lattice Fermi-Hubbard model and observe the dependence of their energy and spectral width on the interaction strength. Finally, we perform exact diagonalization calculations of the expected Raman spectra in the triangular Hubbard system in the highly polarized and low doping limit, previously theoretically explored in the t-J model [10]. Our calculations support ongoing experiments towards the spectroscopic observation of itinerant spin polarons in the frustrated triangular Hubbard model.application/pdfenPrinceton University Senior Theses