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.
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.
Cold atoms with laser-induced spin-orbit (SO) interactions provide a platform to explore quantum physics beyond natural conditions of solids. Here we propose and experimentally realize two-dimensional (2D) SO coupling and topological bands for a rubidium-87 degenerate gas through an optical Raman lattice, without phase-locking or fine-tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including topological superfluids.
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.
Ultra-cold quantum gases subjected to light-induced synthetic gauge potentials have become an emergent field of theoretical and experimental studies. Because of the novel application of two-photon Raman transitions, ultra-cold neutral atoms behave like charged particles in magnetic field. The Raman coupling naturally gives rise to an effective spin-orbit interaction which couples the atom’s center-of-mass motion to its selected pseudo-spin degrees of freedom. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc., we are truly in an exciting era of ful- filling and going beyond Richard Feynman’s vision of realizing quantum simulators to better understand the quantum mechanical nature of the universe, manifested immensely in the ultra-cold regimes. In this dissertation, we present a collection of theoretical progresses made by the doctoral candidate and his colleagues and collaborators. From the past few years of work, we mainly address three aspects of the synthetic spin-orbit and light field induced coupling in ultracold quantum gases: a) The ground-state physics of single- particle system, two-body bound states, and many-body systems, all of which are subjected to spin-orbit coupling originated from synthetic gauge potentials; b) The symmetry breaking, topological phase transition and quench dynamics, which are conveniently offered by the realized experimental setup; c) The proposal and impli- cations of light field induced dynamical spin-orbit coupling for atoms inside optical cavity. Our work represents an important advancement of theoretical understanding to the active research frontier of ultra-cold atom physics with spin-orbit coupling.
Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.
We study quantum phases and transitions in ultra-cold quantum gases, beyond the scope of conventional condensed matter systems. The study focuses on three major thrusts. The first thrust is the study of cold ensembles of bosonic or fermionic atoms in the higher orbital bands of optical lattices. Orbital and topological quantum physics is systematically explored for various lattice geometries, to be outlined below. The second is the low dimensional spin-imbalanced fermions in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We analyze its thermal instability towards Berezinsky-Kosterlitz-Thouless (BKT) phase transitions driven by different topological defects at finite temperature. The third is the theoretical search for a mechanism to achieve a Bose-Einstein crystal phase for bosons in the ground state. A new class of two-body interactions characterized by strong momentum-dependence is found to give rise to such a quantum state. It is different than but related to the long-debated concept of supersolidity. The first thrust forms the main part of the dissertation. Meta-stable phases of high orbital bosons and fermions have been explored for different lattice geometries such as square and bipartite lattices. Exotic Mott and superfluid phases are studied in both one and two dimensions. Quantum and thermal phase transitions, associated with time reversal symmetry breaking and their experimental signatures are discussed. In particular a quantum ``disordered" superfluid phase, beyond the mean field description, is found in one dimension. The challenging problem of probing time reversal symmetry breaking is solved. Besides, a one-dimensional fermionic optical ladder with coupled s- and p-orbitals is shown to mimic spin-orbit interactions and exhibit topological insulator and topological superconducting phases. Charge fractionalization is shown to be realizable in such an sp-orbital ladder.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.