Topological phases of ultracold atoms recently have been intensively studied in both optical superlattices and Raman lattices. However, the topological features induced by the interplay between such two lattices remain largely unexplored. Here we present an optical Raman superlattice system that incorporates an optical superlattice and a Raman superlattice. The Raman superlattice presented here supports tunable dimerized spin-orbit couplings and staggered on-site spin flips. We find that such a system respects a spin-rotation symmetry and has much richer topological properties. Specifically, we show that various topological phases could emerge in the optical Raman superlattice, such as four different chiral topological insulator phases and two different quantum spin Hall insulator phases, identified by spin winding and spin Chern numbers, respectively. We also demonstrate that the spin-dependent topological invariants could be directly measured by quench dynamics.
Topological phases of ultracold atoms recently have been intensively studied in both optical superlattices and Raman lattices. However, the topological features induced by the interplay between such two lattices remain largely unexplored. Here we present an optical Raman superlattice system that incorporates an optical superlattice and a Raman superlattice. The Raman superlattice presented here supports tunable dimerized spin-orbit couplings and staggered on-site spin flips. We find that such a system respects a spin-rotation symmetry and has much richer topological properties. Specifically, we show that various topological phases could emerge in the optical Raman superlattice, such as four different chiral topological insulator phases and two different quantum spin Hall insulator phases, identified by spin winding and spin Chern numbers, respectively. We also demonstrate that the spin-dependent topological invariants could be directly measured by quench dynamics.
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.
We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-1/2 atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the s-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.
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 propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.
Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.
Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multiorder topological superfluids that support various Majorana zero modes in ultracold atomic gases. For this purpose, we use the two-dimensional optical superlattice that introduces a spatial modulation to the spin-orbit coupling in one direction, providing an extra degree of freedom for the emergent higher-order topological state. We find the topologically trivial superfluids, first-order and second-order topological superfluids, as well as different topological phase transitions among them with respect to the experimentally tunable parameters. Besides the conventional transition characterized by the Chern number associated with the bulk gap closing and reopening, we find the system can support the topological superfluids with Majorana corner modes, but the topological phase transition undergoes no gap-closing of bulk bands. Instead, the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge states. The proposal is based on the s-wave interaction and is valid using existing experimental techniques, which unifies multiorder topological phase transitions in a simple but realistic system.