Ultracold atoms offer a versatile platform to study novel quantum phenomena in many-body systems. This platform provides flexible detection and unprecedented controllability with easily accessible experimental parameters. Furthermore, we can implement multi-dimensional lattice potential, tune s-wave interactions, and create various mechanisms including orbital exchange interactions, spin-orbit couplings and artificial gauge field. With those tools in hand, various novel quantum materials have been simulated with ultracold atoms.

In the first part of the thesis, we studied the interaction properties of SU(N)-symmetric fermions that are difficult to be examined in nature. We demonstrate an evidence of Bosonization in three-dimensional(3D) by measuring Tan's contact in the momentum distri...[ Read more ]

Ultracold atoms offer a versatile platform to study novel quantum phenomena in many-body systems. This platform provides flexible detection and unprecedented controllability with easily accessible experimental parameters. Furthermore, we can implement multi-dimensional lattice potential, tune s-wave interactions, and create various mechanisms including orbital exchange interactions, spin-orbit couplings and artificial gauge field. With those tools in hand, various novel quantum materials have been simulated with ultracold atoms.

In the first part of the thesis, we studied the interaction properties of SU(N)-symmetric fermions that are difficult to be examined in nature. We demonstrate an evidence of Bosonization in three-dimensional(3D) by measuring Tan's contact in the momentum distribution of high-spin fermions of ¹⁷³Yb. We find contact per spin of SU(N) Fermi gas saturates to bosonic limit in large N limit. We also measure collective modes of a two-dimensional(2D) SU(N) Fermi gas showing its' quadrupole frequency decreases with increasing N. The result implies that effective interaction strength in a SU(N) Fermi gas can be amplified by SU(N) symmetry. Those measurements pave the way to study SU(N) symmetric system with ultracold atoms.

In the second part of the thesis, quantum simulation has been extended to topological matter. We simulate 1D spin-orbit coupled Raman lattice system, which is an optical lattice with Raman coupling fields. Novel symmetry-protected topological bands are detected by measuring spin texture. We reveal the band topology both from in-equilibrium spin textures and spin dynamics after quench. We further realize a 3D nodal line semimetal. We demonstrate an effective tomography of 3D band structure by changing Zeeman energy. Nodal lines are reconstructed from a sequence of spin texture measurements. The existence of band inversion lines, which connect Dirac points, are confirmed with quench dynamics.

Finally, I explain technical improvement of our laser locking stability, magneto-optical trap (MOT) loading efficiency, evaporation cooling and absorption imaging quality. I also show our first observation of clock transition in our ytterbium system. With those improvements, we envision simulating more complex and unprecedented quantum systems, such as Kondo lattice model.