Topologically protected states are observed in engineered optical lattices with ultracold fermions.

We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of 173 Yb atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the SU(N ) symmetry of the 1 S0 ground-state manifold which is insensitive to external magnetic fields, an optical AC Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali and lanthanide atoms, and separate out an effective spin-1/2 subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynamics when a momentum-dependent spin-orbit gap being suddenly opened and the asymmetric momentum distribution of the spin-orbit coupled Fermi gas are observed as a hallmark of SOC. The realization of all-optical SOC for ytterbium fermions should offer a new route to a long-lived spin-orbit coupled Fermi gas and greatly expand our capability in studying novel spin-orbit physics with alkaline-earth-like atoms.Ultracold atoms are fascinating for the study of synthetic quantum system which is direct analogy to real electronic material [1]. One of the notable examples is the implementation of synthetic gauge field and spinorbit coupling (SOC) engineered with the atom-light interaction at will [2,3]. In particular, SOC links a particle's spin with its momentum, which is not only essential in novel quantum phenomena, such as spintronic effect [4] and exotic topological states of quantum matter [5,6], but also provides an unprecedented quantum system such as spin-half spin-orbit coupled bosons without analogy in condensed-matter [7]. Various types of SOCs can be generated in ultracold atoms where the relevant parameters are tunable by changing the laser fields [8][9][10] or the magnetic field [11]. So far, the SOCs along the one direction have been created in bosonic alkali [7,[12][13][14][15][16][17][18][19], fermionic alkali atoms [20][21][22][23], and very recently in fermionic lanthanide atoms [24]. Besides the 1D SOC, the two-dimensional synthetic SOCs have been also demonstrated both in the bosonic [25] and fermionic alkali atoms [26].In alkali atoms, two different internal states are coupled through the Raman transition transferring momentum to the atoms [2,3]. However those processes inevitably suffer from heating effect caused by spontaneous emission due to the small fine-structure splitting of the excited level, which could limit the ability to observe interacting many-body phenomena that needs long timescales. Recently to avoid such heating, the specific atomic species with the large ground-state angular momentum such as 161 Dy have been considered [27,28] or the external orbital states, representing pseudo-spins, in optical superlattices have been used to generate SOC [29,30].Here, we expand our capability in exploring a novel SOC physics by implementing SOC with a narrow optical transition in a non-alkali Fermi gas of ytterbium atoms. With a momentum-dependent spin-orbit gap being suddenly opened by switching on the Raman transitio...

Observation of topological phases beyond twodimension (2D) has been an open challenge for ultracold atoms. Here, we realize for the first time a 3D spin-orbit coupled nodal-line semimetal in an optical lattice and observe the bulk line nodes with ultracold fermions. The realized topological semimetal exhibits an emergent magnetic group symmetry. This allows to detect the nodal lines by effectively reconstructing the 3D topological band from a series of measurements of integrated spin textures, which precisely render spin textures on the parameter-tuned magnetic-groupsymmetric planes. The detection technique can be generally applied to explore 3D topological states of similar symmetries. Furthermore, we observe the band inversion lines from topological quench dynamics, which are bulk counterparts of Fermi arc states and connect the Dirac points, reconfirming the realized topological band. Our results demonstrate the first approach to effectively observe 3D band topology, and open the way to probe exotic topological physics for ultracold atoms in high dimensions.The past decade has witnessed great progresses in search for topological quantum phases, in particular the topological insulators [1, 2] and semimetals [3][4][5][6][7] in solid state materials which commonly have strong spinorbit (SO) couplings. Among the topological phases, a semimetal phase has gapless bulk nodes protected by symmetry and topology [8,9]. Particularly, the nodalline semimetal has degenerate bulk quasiparticles extending 1D line [10,11], and can serve as a parent phase to further realize exotic states including Weyl semimetals and topological insulators. Unlike the boundary modes of a topological matter which can be resolved with transport measurements or ARPES technique [1,2], the bulk topology is usually harder to detect. For nodal-line semimetals, the line-shape nodes of solids are embedded in the 3D band structure and their direct imaging could be im- * These authors contributed equally to this work. † Electronic address: xiongjunliu@pku.edu.cn ‡ Electronic address: gbjo@ust.hk