Abstract

Ultracold atoms provide a controllable platform to explore topological matters induced by spin-orbit (SO) coupling. This thesis reports an experimental realization of topological matters with Ytterbium atoms approached by a Raman (or SO coupling) lattice — an optical lattice dressed by SO coupling, where internal atomic states are coupled by Raman beams. Remarkably, the lattice simultaneously serves as one of Raman beams.

As the building block of the Raman lattice, SO coupling is first studied in a one-dimensional (1D) bulk system and manifested by two hallmarks, the lock between the atomic spin and momentum, and the dephasing in the Rabi oscillation, respectively.

SO in a periodic lattice renders topological features. 1D Raman lattice showcases a novel symmetry-protected topological (SPT) phase beyond the tenfold Altland-Zirnbauer classification. SPT phases are distinguished by the Z₂ invariant determined from spin-textures. We highlight that textures not only in equilibrium, but also of dynamics far from equilibrium, after the quench between two distinct phases, reflect the band topology.

Furthermore, higher dimensional Raman lattices are more fruitful. A three-dimensional (3D) topological nodal line semimetal structure has been observed for the first time with ultracold atoms, and reconstructed by a well-designed (pseudo-) tomography — extraction of Dirac points on different momentum layers, thanks to the emergence of a crystalline symmetry. Similarly, topological features, such as band inversion lines that are bulk counterparts of Fermi arc states and connect Dirac points, are also uncovered from quench dynamics.

More is different. The SU(N) symmetric spin-independent interaction is exploited by Tan contact and collective modes. Enhanced by the (orbital) Feshbach resonance, the Raman lattice with tunable interactions can be applied to engineer elusive topological many-body phases, which is envisaged for unveiling attractive topological superfluids.