RESUMEN
We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with a topological nontrivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the antisymmetric Raman lattice structure, and generate the 2D SO coupling with precise inversion and C_{4} symmetries, leading to considerably enlarged topological regions. The lifetime of the 2D SO coupled Bose-Einstein condensate reaches several seconds, which enables exploring fine-tuning interaction effects. These essential advantages of the present new realization open the door to explore exotic quantum many-body effects and nonequilibrium dynamics with novel topology.
RESUMEN
Topological quantum states are characterized by nonlocal invariants. We present a new dynamical approach for ultracold-atom systems to uncover their band topology, and we provide solid evidence to demonstrate its experimental advantages. After quenching a two-dimensional (2D) Chern band, realized in an ultracold ^{87}Rb gas from a trivial to a topological parameter regime, we observe an emerging ring structure in the spin dynamics during the unitary evolution, which uniquely corresponds to the Chern number for the postquench band. By extracting 2D bulk topology from the 1D ring pattern, our scheme displays simplicity and is insensitive to perturbations. This insensitivity enables a high-precision determination of the full phase diagram for the system's band topology.
RESUMEN
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size L=4096, and study the geometric properties of the flow configurations. As the coupling strength K increases, we observe that the system undergoes a percolation transition K_{perc} from a disordered phase consisting of small clusters into an ordered phase containing a giant percolating cluster. Namely, in the low-temperature phase, there exhibits a long-ranged order regarding the flow connectivity, in contrast to the quasi-long-range order associated with spin properties. Near K_{perc}, the scaling behavior of geometric observables is well described by the standard finite-size scaling ansatz for a second-order phase transition. The estimated percolation threshold K_{perc}=1.1053(4) is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point K_{BKT}=1.1193(10), which is determined from the magnetic susceptibility and the superfluid density. Various interesting questions arise from these unconventional observations, and their solutions would shed light on a variety of classical and quantum systems of BKT phase transitions.
RESUMEN
Weyl semimetals are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band. According to lattice theory, Weyl cones must come in pairs, with the minimum number of cones being two. A semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM). Here we report the experimental realization of an IWSM band by engineering 3D spin-orbit coupling for ultracold atoms. The topological Weyl points are clearly measured via the virtual slicing imaging technique in equilibrium and are further resolved in the quench dynamics. The realization of an IWSM band opens an avenue to investigate various exotic phenomena that are difficult to access in solids.
RESUMEN
There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional (3D) spin-orbit (SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics.
RESUMEN
To investigate the band structure is one of the key approaches to study the fundamental properties of a novel material. We report here the precision band mapping of a 2-dimensional (2D) spin-orbit (SO) coupling in an optical lattice. By applying the microwave spin-injection spectroscopy, the band structure and spin-polarization distribution are achieved simultaneously. The band topology is also addressed with observing the band gap close and re-open at the Dirac points. Furthermore, the lattice depth and the Raman coupling strength are precisely calibrated with relative errors in the order of 10-3. Our approach could also be applied for exploring the exotic topological phases with even higher dimensional system.
RESUMEN
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.