Recent experimental realization of one-dimensional spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline-earth atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin distributions of such topological bands for 2D Rashba and 3D Weyl SOCs can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.
Recent experimental realization of one-dimensional spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline-earth atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin distributions of such topological bands for 2D Rashba and 3D Weyl SOCs can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.
We propose a hierarchy set of minimal optical Raman lattice schemes to pave the way for experimental realization of high-dimensional spin-orbit (SO) couplings for ultracold atoms, including two-dimensional (2D) Dirac type, 2D Rashba type, and three-dimensional (3D) Weyl type. The proposed Dirac-type SO coupling exhibits precisely controllable high symmetry, for which a large topological phase region is predicted. The generation of 2D Rashba and 3D Weyl types requires that two sources of laser beams have distinct frequencies of factor 2 difference. Surprisingly, we find that 133Cs atoms provide an ideal candidate for the realization. A common and essential feature is of high controllability and absent of any fine-tuning in the realization, and the resulting SO coupled ultracold atoms have a long lifetime. In particular, a long-lived topological Bose gas of 2D Dirac SO coupling has been proved in the follow-up experiment. These schemes essentially improve over the current experimental accessibility and controllability, and open a realistic way to explore novel high-dimensional SO physics, particularly quantum many-body physics and quantum far-from-equilibrium dynamics with novel topology for ultracold atoms.
The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid-state materials such as SO-coupled pseudospin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Rashba-type SO coupling in a square lattice for pseudospin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid-state materials. These exotic phases include triply degenerate points, quadratic band touching, a large Chern number (C=5) superfluid with five Majorana modes, triple-Weyl fermions, and so on. Our scheme can be generalized to larger spins and provides a distinctive route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.
The recent experimental realization of synthetic spin-orbit coupling (SOC) opens a new avenue for exploring novel quantum states with ultracold atoms. However, in experiments for generating two-dimensional SOC (e.g., Rashba type), a perpendicular Zeeman field, which opens a band gap at the Dirac point and induces many topological phenomena, is still lacking. Here, we theoretically propose and experimentally realize a simple scheme for generating two-dimensional SOC and a perpendicular Zeeman field simultaneously in ultracold Fermi gases by tuning the polarization of three Raman lasers that couple three hyperfine ground states of atoms. The resulting band gap opening at the Dirac point is probed using spin injection radio-frequency spectroscopy. Our observation may pave the way for exploring topological transport and topological superfluids with exotic Majorana and Weyl fermion excitations in ultracold atoms.
Weyl points, synthetic magnetic monopoles in the three-dimensional momentum space, are the key features of topological Weyl semimetals. The observation of Weyl points in ultracold atomic gases usually relies on the realization of high-dimensional spin-orbit coupling (SOC) for two pseudospin states (i.e., spin 1/2), which requires complex laser configurations and precise control of laser parameters, thus, has not been realized in experiment. Here, we propose that robust Weyl points can be realized using one-dimensional triple-well superlattices (spin-1/three-band systems) with two-dimensional transverse SOC achieved by Raman-assisted tunnelings. The presence of the third band is responsible to the robustness of the Weyl points against system parameters (e.g., Raman laser polarization, phase, incident angle, etc.). Different from a spin-1/2 system, the nontrivial topology of Weyl points in such spin-1 system is characterized by both spin vector and tensor textures, which can be probed using momentum-resolved Rabi spectroscopy. Our proposal provides a simple yet powerful platform for exploring Weyl physics and related high-dimensional topological phenomena using high pseudospin ultracold atoms.
Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.
Exploring 3D topological matter with spin-orbit-coupled fermions in optical lattices1 CHENGDONG HE, BO SONG, Hong Kong University of Science and Technology, SEN NIU, LONG ZHANG, Peking University, ZEJIAN REN, ENTONG ZHAO, Hong Kong University of Science and Technology, XIONG-JUN LIU, Peking University, GYU-BOONG JO, Hong Kong University of Science and Technology — Ultracold atoms offer a promising testbed for the experimental study of topological matter. Various topological models have been recently realized in 1D and 2D atomic systems. While 3D topological matter with rich physics remains unexplored due to experimental complexity. Here we report, for the first time, the realization of a 3D nodal line semimetal in optical lattices with SO coupled ultracold fermions. The 3D topological band structure is achieved by stacking 2D Dirac semimetal in the x-y plane along z direction in Raman-dressed optical lattices. kz resolved spin texture measurement technique based on emergent magnetic group symmetry has been developed to detect 3D topological state. Spin texture in a specific kz plane can be directly imaged with different Zeeman splitting. 3D nodal lines can be reconstructed with this pseudo-tomography method. Band inversion lines, the bulk counterparts of Fermi arc states, can be extracted from quench dynamics, which reconfirmed the realization of topological phase. Our detection technique can be broadly applied to characterizing 3D topological states with similar symmetries, which provides a new possibility to study exotic quantum physics in higher dimensions.