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Bulletin of the American Physical Society

Exploring 3D topological matter with spin-orbit-coupled fermions in optical lattices

Chengdong He, Bo Song, Sen Niu, Long Zhang, Zejian Ren, Entong Zhao, Xiong-Jun Liu, Gyu-Boong Jo

Published May 29, 2019• 0 citations
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Abstract

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.

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Realization of three-dimensional nodal-line semimetal with ultracold fermions

Chengdong He, Bo Song, Sen Niu +5 more

Despite recent breakthroughs in topological bands for ultracold atoms in 1D and 2D, it has been an open challenge to realize and observe 3D topological matter in an atomic system. While numerous schemes have been proposed, the experimental complexity and the characterization of the 3D band structure acted as a barrier against experimental groups achieving this outstanding goal. In this talk, we report the realization and observation of 3D nodal-line semimetal band with spin-orbit-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. To detect 3D topological phases, we developed kz resolved spin texture measurement technique based on emergent magnetic group symmetry in our system. By directly imaging spin texture in specific kz plane with different Zeeman splitting, 3D nodal lines can be reconstructed. The realization of topological band structure is also verified in quench dynamics by detecting band inversion lines, which are bulk counterparts of Fermi arc states. This technique can be broadly applied to characterizing 3D topological states with similar symmetries.

Bulletin of the American Physical Society•May 29, 2019•0 citations

Topological matter in ultracold ytterbium quantum gases with spin-orbit coupling

Bo Song

Ultracold atoms provide a controllable platform to explore topological matter induced by spin-orbit (SO) coupling. This thesis reports an experimental realization of topological matter with Ytterbium atoms implemented 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 the 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 locking between the atomic spin and momentum and the dephasing in the Rabi oscillation. SO coupling in a periodic lattice renders topological matter. 1D Raman lattice show-cases a novel symmetry-protected topological (SPT) phase beyond the tenfold Altland-Zirnbauer classification. SPT phases distinguished by the Z2 invariant are determined from spin-textures. We highlight textures not only in equilibrium, but also of far-from-equilibrium dynamics after a quench between distinct phases, reflecting the band topology. Higher dimensional Raman lattices are richer. 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, owing 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 investigated by Tan's 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 the attractive topological superfuilds.

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Rashba and Weyl spin-orbit coupling in an optical lattice clock

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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.

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Spin-orbit Coupling and Topological Phases for Ultracold Atoms

Long Zhang, Xiong-Jun Liu

Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.

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Exploring topological double-Weyl semimetals with cold atoms in optical lattices

Xue-Ying Mai, Dan-Wei Zhang, Zhi Li +1 more

We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the ${C}_{4h}$ point-group symmetry. By applying a realizable ${C}_{4}$ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the ${C}_{4}$ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the ${C}_{4}$-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.

arXiv:1706.02063•Physical Review A•Jun 21, 2017•24 citations
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.
Despite recent breakthroughs in topological bands for ultracold atoms in 1D and 2D, it has been an open challenge to realize and observe 3D topological matter in an atomic system. While numerous schemes have been proposed, the experimental complexity and the characterization of the 3D band structure acted as a barrier against experimental groups achieving this outstanding goal. In this talk, we report the realization and observation of 3D nodal-line semimetal band with spin-orbit-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. To detect 3D topological phases, we developed kz resolved spin texture measurement technique based on emergent magnetic group symmetry in our system. By directly imaging spin texture in specific kz plane with different Zeeman splitting, 3D nodal lines can be reconstructed. The realization of topological band structure is also verified in quench dynamics by detecting band inversion lines, which are bulk counterparts of Fermi arc states. This technique can be broadly applied to characterizing 3D topological states with similar symmetries.
Ultracold atoms provide a controllable platform to explore topological matter induced by spin-orbit (SO) coupling. This thesis reports an experimental realization of topological matter with Ytterbium atoms implemented 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 the 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 locking between the atomic spin and momentum and the dephasing in the Rabi oscillation. SO coupling in a periodic lattice renders topological matter. 1D Raman lattice show-cases a novel symmetry-protected topological (SPT) phase beyond the tenfold Altland-Zirnbauer classification. SPT phases distinguished by the Z2 invariant are determined from spin-textures. We highlight textures not only in equilibrium, but also of far-from-equilibrium dynamics after a quench between distinct phases, reflecting the band topology. Higher dimensional Raman lattices are richer. 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, owing 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 investigated by Tan's 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 the attractive topological superfuilds.
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.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4h{C}_{4h}C4h​ point-group symmetry. By applying a realizable C4{C}_{4}C4​ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4{C}_{4}C4​ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the C4{C}_{4}C4​-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.