Quantum Gas Microscopy of Frustrated Quantum Many-Body Systems

Quantum gas microscopy has played an important role in the understanding of many-particle physics in strongly correlated systems. The single-atom-resolved imaging enables the detection of microscopic properties on many-fermion systems on the single site level in the quantum regime. Relying on the unique tunability of ultracold atoms in atomic interactions via Feshbach resonances, density, and spin imbalance, a wide parameter range in the phase diagram can be explored. Some of the theoretically most challenging systems with rich phase diagrams are frustrated systems. Triangular lattices are the simplest example of geometric frustration in which three spins with antiferromagnetic interactions cannot be antiparallel, leading to a large degeneracy in the many-body ground state and could result in quantum spin liquids.
In this dissertation, I report on the development of a triangular-lattice quantum gas microscope and the study of geometrically frustrated Mott insulators. The microscope enables us to detect unprecedented details of Hubbard physics in the geometrically frustrated system through imaging of the occupation, the spin density, and spin correlation functions on the single site level. I present the first realization of a Mott insulator of lithium-6 on a symmetric triangular lattice with a lattice spacing of 1003 nm. For the first time, we image fermionic lithium in a triangular lattice via a Raman sideband cooling technique with an imaging fidelity of 98%. In addition, we measure spin-spin correlations and observe nearest-neighbor anticorrelations consistent with short-range 120 degree order. We find a good agreement between the results and simulations (Determinantal Quantum Monte Carlo [DQMC] and Numerical Linked- Cluster Expansion [NLCE]). In addition, spin-resolved density is implemented in a square lattice, allowing us to obtain all information on the density in the system and direct measurement of spin-spin correlations.
By utilizing spin-resolved imaging, we explore a three-component Fermi-Hubbard model with imbalanced interactions between spin components. Our observations reveal a signature of a Mott insulator state through the variance of density and compressibility. We examine the interplay between the different spin components through pairing correlations. This study opens possibilities for simulating physics beyond condensed matter models by realizing three-component Fermi lattice gases. Quantum gas microscope expands our understanding of exotic phenomena in materials, such as high-temperature superconductors from first principles in tunable systems. Our microscope offers a platform for exploring nuclear physics, including the formation of baryons and their superfluidity, through ultracold-atom systems. Additionally, the capabilities of the microscope in studying quantum spin liquids hold promise for the discovery of new quantum phases.