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 ...

Unique spindle-shaped nanoporous anatase TiO(2) mesocrystals with a single-crystal-like structure and tunable sizes were successfully fabricated on a large scale through mesoscale assembly in the tetrabutyl titanate-acetic acid system without any additives under solvothermal conditions. A complex mesoscale assembly process involving slow release of soluble species from metastable solid precursors for the continuous formation of nascent anatase nanocrystals, oriented aggregation of tiny anatase nanocrystals, and entrapment of in situ produced butyl acetate as a porogen was put forward for the formation of the anatase mesocrystals. It was revealed that the acetic acid molecules played multiple key roles during the nonhydrolytic processing of the [001]-oriented, single-crystal-like anatase mesocrystals. The obtained nanoporous anatase mesocrystals exhibited remarkable crystalline-phase stability (i.e., the pure phase of anatase can be retained after being annealed at 900 °C) and improved performance as anode materials for lithium ion batteries, which could be largely attributed to the intrinsic single-crystal-like nature as well as high porosity of the nanoporous mesocrystals.

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A single photon source is realized with a cold atomic ensemble ( 87 Rb atoms). In the experiment, single photons, which is initially stored in an atomic quantum memory generated by Raman scattering of a laser pulse, can be emitted deterministically at a time-delay in control. It is shown that production rate of single photons can be enhanced by a feedback circuit considerably while the single-photon quality is conserved. Thus our present single-photon source is well suitable for future large-scale realization of quantum communication and linear optical quantum computation.PACS numbers: 03.67. Hk, 32.80.Pj, 42.50.Dv Although weak coherent beams can be used as a pseudo single-photon source, the advent of quantum information processing (QIP) has placed stringent requirements on single photons either on demand or heralded [1]. In particular, secure quantum cryptography [2] and linear optical quantum computing [3] depend on the availability of such single-photon sources. Different approaches have been attempted in the last decade to develop the on-demand single-photon source, such as the implementations with quantum dots [4,5], single atoms and ions [6,7], and color centers [8]. However, all of them are confronted with different challenges. For example, the single-atom implementation provides spectrally narrow single photons with a well defined spatial mode, but the main challenge is the manipulation of single atoms, which requires sophisticated and expensive setups [6]. Although quantum dots present many advantages as potential source of single photons, e.g. high single-photon rate, the requirement of spectral filtering entails inevitable losses. Additionally, it is a major problem for preparing truly identical sources due to inhomogeneities in both the environment of the emitters and the emitters itself [9]. The stability of color centers is excellent, even at room temperature. However, the high peak intensities of a pulsed excitation can lead to complex and uncontrollable dark states [1]. So it has been taken as a formidable task to develop a promising single-photon source.Moreover, an important challenge in distributed QIP is the controllable transfer of quantum state between flying qubit and macroscopic matter. Remarkably, as shown in a recent proposal for long-distance quantum communication with atomic ensembles [10], it is possible to implement both a single-photon source on demand and the controllable transfer of quantum state between photonic qubit and macroscopic matter, provided that proper feedback is applied to achieve the classical feed-forward ability. Such feed-forward ability is a crucial requirement in linear optics QIP [3,10]. In other words, it must be, in principle, possible to detect when an operation has succeeded by performing some appropriate measurement on ancilla photons. This information can then be feed-forwarded for conditional future operations on the photonic qubits to achieve efficient QIP.Recently, significant experimental progresses have been achieved in demonstration of quantum ...

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We report the heralded generation of an atomic NOON state by observation of phase super resolution in a motion-sensitive spin-wave (SW) interferometer. The SW interferometer is implemented by generating a superposition of two SWs and observing the interference between them, where the interference fringe is sensitive to the atomic collective motion. By heralded generation of a second order NOON state in the SW interferometer, we observe the interference pattern which provides strong evidence of phase super resolution. The demonstrated SW interferometer can in principle be scaled up to a highly entangled state, and thus is of fundamental importance, and might be used as an inertial sensor.

We propose a hierarchy set of minimal optical Raman lattice schemes toward the experimental realization of spin-orbit (SO) couplings of various types for ultracold atoms, including two-dimensional (2D) Dirac type of C4 symmetry, 2D Rashba and 3D Weyl types. These schemes are well accessible with current cold-atom technology, and in particular, a long-lived Bose-Einstein condensation of the 2D Dirac SO coupling has been experimentally proved. The generation of 2D Rashba and 3D Weyl types has an exquisite request that two sources of laser beams have distinct frequencies of factor-two difference. Surprisingly, we find that 133 Cs atoms provide an ideal candidate for the realization. A common and essential feature is the absence of any fine-tuning and phase-locking in the realization, and the resulted SO coupled ultracold atoms have a long lifetime. These schemes essentially improve over the current experimental accessibility and controllability, and open new experimental platforms to study high-dimensional SO physics and novel topological phases with ultracold atoms.Topological phase of matter has become a mainstream of research in condensed matter physics. Recent outstanding examples include topological insulators, which have been predicted and experimentally discovered in two-dimensional (2D) and 3D materials [1, 2], topological semimetals, which exhibit linear dispersion around nodes termed the Dirac or Weyl points, were found recently in a number of materials like Cd 3 As 2 [3, 4] and TaAs [5,6], and topological superconductors [7-10], which host exotic zero-energy states called Majorana modes and have attracted considerable experimental efforts [11][12][13][14][15][16][17]. In these matters, the spin-orbit (SO) interactions, manifesting Dirac, Rashba and Weyl types, play essential roles in driving the phases to be topologically nontrivial.Very recently, the experimental realizations of 2D SO couplings have been respectively reported in 87 Rb Bose-Einstein condensate (BEC) [18] and 40 K degenerate Fermi gases [19,20], where nontrivial band topology and Dirac point are observed. The reports signify an important achievement in the field of quantum simulator with ultracold atoms and optical lattice, opening a great deal of possibilities to explore novel quantum states beyond natural conditions [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Nevertheless, the current experiments suffer challenges in controllability, since the realizations rely on the blue-detuned optical lattices [18,27] or delicate manipulation of resonant Raman couplings between multiple ground states [19,20]. To be broadly applicable to studying exotic topological phases mentioned above, the SO coupled systems should exhibit the following criteria, the high controllability and high stability with long lifetime, which however cannot be satisfied in the current experiments.In this Letter, we propose a hierarchy set of min-" # % , % ( , ( %, %( (% (, | ↓ ⟩ | ↑ ⟩ Atom Cloud | " ⟩ | # ⟩ (a) (b) DB DB Δ Mirror FIG. 1: (a) Generic setup fo...