A system of ultracold atoms in an optical lattice is an ideal quantum simulator of a strongly correlated quantum many-body system [1]. Ultracold fermions with an enlarged spin symmetry of SU(N) offer novel possibilities of quantum simulation [2]. In particular, recent theories for an SU(N) Fermi-Hubbard model predict novel quantum magnetisms. I will present our study of an SU(N=6) Fermi-Hubbard model by working with ultracold two-electron atoms of ytterbium. By developing an all-optical means of singlet-triplet oscillation, we successfully detect nearest-neighbor spin correlations in various lattice geometries. Importantly, this enlarged spin symmetry of SU(N) is a powerful tool to lower the temperature of atoms in an optical lattice, known as a Pomeranchuk cooling effect. The detailed comparison between theory and experiment allows us to infer the realization of a lowest temperature of cold-atom Fermi-Hubbard model in one dimension [3]. I will also present the experiments with a plaquette lattice configuration with various spin imbalances and intra- to inter-plaquette hopping ratios, including the realization of a novel four-body entangled state of SU(4)-singlet, and the quantum magnetism in an open dissipative Fermi-Hubbard system.
[1] F. Schäfer et al., “Tools for quantum simulation with ultracold atoms in optical lattices”
Nat. Rev. Phys. 2, 411 (2020).
[2] M. A. Cazalilla and A. M. Rey, “Ultracold Fermi gases with emergent SU(N) symmetry”
Rep. Prog. Phys. 77,124401 (2014).
[3] S. Taie, E. Ibarra-García-Padilla, N. Nishizawa, Y. Takasu, Y. Kuno, H-T. Wei, R. T. Scalettar, K. R. A. Hazzard, and Y. Takahashi, “Observation of antiferromagnetic correlations in an ultracold SU(N) Hubbard model”,arXiv:2010.07730.