Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion gases. However, realization of 2D SO interaction, a much more important task, remains very challenging.Here we propose and experimentally realize, for the first time, 2D SO coupling and topological band with 87 Rb degenerate gas through a minimal optical Raman lattice scheme, without relying on 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 the momentum 1 arXiv:1511.08170v1 [cond-mat.quant-gas] 24 Nov 2015space. 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 the highly-sought-after topological superfluid phases.Spin-orbit (SO) interaction of an electron is a relativistic quantum mechanic effect, which characterizes the coupling between motion and spin of the electron when moving in an electric field. In the rest frame the electron experiences a magnetic field which is proportional to the electron velocity and couples to its spin by the magnetic dipole interaction, rendering the SO coupling. The SO interaction plays essential roles in many novel quantum states of solids. The recent outstanding examples include the topological insulators, which have been predicted and experimentally discovered in two-dimensional (2D) and 3D materials 1, 2 , and the topological superconductors 3, 4 , which host exotic zero-energy states called Majorana fermions 5,6 and still necessitate rigorous experimental verification. For topological insulators, the strong SO interaction leads to the so-called band inversion mechanism which drives a topological phase transition in such systems 7,8 . In superconductors, a triplet p-wave pairing is generically resulted when SO coupling is present, for which the superconductivity can be topologically nontrivial under proper conditions 9 .Recently, considerable interests have been drawn in emulating SO effects and topological phases with cold atoms, mostly driven by the fact that cold atoms can offer extremely clean platforms with full controllability to explore such exotic physics. In cold atoms the synthetic SO interaction can be generated by Raman coupling schemes which flip atom spins and transfer momentum where 1 is the 2 × 2 unit matrix, σ x,y,z are Pauli matrices acting on the spins, m is mass of an atom, V latt denotes the lattice potential in the x-z plane, M x,y are periodic Raman coupling potentials, and m z represents a tunable Zeeman field. Atoms can hop between nearest-neighboring sites due to lattice potential as well as the Raman coupling terms. Note that V latt is spin-independent and can induce hopping which conserves ...

Next-generation high-performance structural materials are required for lightweight design strategies and advanced energy applications. Maraging steels, combining a martensite matrix with nanoprecipitates, are a class of high-strength materials with the potential for matching these demands. Their outstanding strength originates from semi-coherent precipitates, which unavoidably exhibit a heterogeneous distribution that creates large coherency strains, which in turn may promote crack initiation under load. Here we report a counterintuitive strategy for the design of ultrastrong steel alloys by high-density nanoprecipitation with minimal lattice misfit. We found that these highly dispersed, fully coherent precipitates (that is, the crystal lattice of the precipitates is almost the same as that of the surrounding matrix), showing very low lattice misfit with the matrix and high anti-phase boundary energy, strengthen alloys without sacrificing ductility. Such low lattice misfit (0.03 ± 0.04 per cent) decreases the nucleation barrier for precipitation, thus enabling and stabilizing nanoprecipitates with an extremely high number density (more than 10 per cubic metre) and small size (about 2.7 ± 0.2 nanometres). The minimized elastic misfit strain around the particles does not contribute much to the dislocation interaction, which is typically needed for strength increase. Instead, our strengthening mechanism exploits the chemical ordering effect that creates backstresses (the forces opposing deformation) when precipitates are cut by dislocations. We create a class of steels, strengthened by Ni(Al,Fe) precipitates, with a strength of up to 2.2 gigapascals and good ductility (about 8.2 per cent). The chemical composition of the precipitates enables a substantial reduction in cost compared to conventional maraging steels owing to the replacement of the essential but high-cost alloying elements cobalt and titanium with inexpensive and lightweight aluminium. Strengthening of this class of steel alloy is based on minimal lattice misfit to achieve maximal precipitate dispersion and high cutting stress (the stress required for dislocations to cut through coherent precipitates and thus produce plastic deformation), and we envisage that this lattice misfit design concept may be applied to many other metallic alloys.

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We propose an experimental scheme to observe spin-orbit coupling effects of a two-dimensional (2D) Fermi atomic gas cloud by coupling its internal electronic states (pseudospins) to radiation in a Lambda configuration. The induced spin-orbit (SO) coupling can be of the Dresselhaus and Rashba type with and without a Zeeman term. We show that the optically induced SO coupling can lead to a spin-dependent effective mass under appropriate condition, with one of them able to be tuned between positive and negative effective masses. As a direct observable we show that in the expansion dynamics of the atomic cloud the initial atomic cloud splits into two clouds for the positive effective mass case regime, and into four clouds for the negative effective mass regime. [3,4]. In correspondence to the spin of an electron, the internal degree of freedom of an atom (pseudospin) is represented by the superposition of its electronic states (hyperfine levels). SO coupling can be equivalently depicted as the interaction between an effective non-Abelian gauge potential and a particle with (pseudo)spin. In quantum systems, the idea generating a gauge field adiabatically was proposed by Wilczek and Zee more than twenty years ago [5]. Recently, such an idea was applied to atomic systems, where the motion of atoms in a position dependent laser configuration gives rise to an effective non-Abelian gauge potential [6,7,8,9,10], which can lead to an effective SO interaction in an ultracold atomic gas [11,12,13].Realization of SO interaction in atomic gases opens new possibility of studying spintronic effects, e.g. spin relaxation [11], Zitterbewegung [12] and SHE, in atomic systems which provide an extremely clean environment, allowing in a controllable fashion unique access to the study of complex physics. However, experimental detection of such SO effects in atoms requires to measure the pseudospins (not just hyperfine levels) that are usually not directly observable for atomic systems. In this letter, we propose an experimental scheme to study SO coupling effects, based on a trapped two-dimensional (2D) Fermi atomic gas with a simple internal three-level Λ-type setup. We demonstrate that an effective SO interaction, e.g. Rashba and linear Dresselhaus terms, can be obtained by coupling atoms with a three-level configuration to spatially varying laser fields. The optically induced SO coupling can lead to a spin-dependent effective masses under proper condition. A direct observable of this effects is in the expansion dynamics for each of the effective mass cases after the external trap is switched off and we predict that the initial atomic cloud splits into two or four clouds.|c>(1/2)Ω We consider a cloud of quasi 2D (y-z plane) Fermi atomic gas with internal three-level Λ-type configuration (see Fig. 1 (a)) coupled to radiation. The transition |b → |a is coupled by the laser field with Rabi-frequency Ω 1 = Ω 10 exp[iφ 1 (r)] and the transition |c → |a is coupled by another laser field Ω 2 = Ω 20 exp[iφ 2 (r)], where φ 1,2 (r) are positi...

Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analogue of graphene, have lately generated widespread interest in both materials science and condensed matter physics. Recently, crystalline Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atmosphere. Here, by using point contact spectroscopy measurements, we observe exotic superconductivity around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric around zero bias suggest p-wave-like unconventional superconductivity. Considering the topological properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topological superconductors, which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material.

We propose to observe and manipulate topological edge spins in a one-dimensional optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In the free-fermion case the SPT phase is classified by a Z invariant which reduces to Z(4) with interactions. The zero edge modes of the SPT phase are spin polarized, with left and right edge spins polarized to opposite directions and forming a topological spin qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in an optical lattice. The manipulation of TSQs has potential applications to quantum computation.

Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete with ongoing challenges in both theory and experiment. Here we propose to establish a universal dynamical characterization of the topological quantum phases classified by integers, and further propose the high-precision dynamical schemes to detect such states. The framework of the dynamical classification theory consists of basic theorems. First, we uncover that classifying a d-dimensional (dD) gapped topological phase of generic multibands can reduce to a (d − 1)D invariant defined on so-called band inversion surfaces (BISs), rendering a bulk-surface duality which simplifies the topological characterization. Further, we show in quenching across phase boundary the (pseudo)spin dynamics to exhibit unique topological patterns on BISs, which are attributed to the post-quench bulk topology and manifest a dynamical bulk-surface correspondence. For this the topological phase is classified by a dynamical topological invariant measured from dynamical spin-texture field on the BISs. Applications to quenching experiments on feasible models are proposed and studied, demonstrating the new experimental strategies to detect topological phases with high feasibility. This work opens a broad new direction to classify and detect topological phases by quantum dynamics. arXiv:1802.10061v3 [cond-mat.mes-hall]

We propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental set-ups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.