Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double well potential

We investigate the quantum dynamics of an experimentally realized spin-orbit coupled Bose-Einstein condensate in a double well potential. The spin-orbit coupling can significantly enhance the atomic inter-well tunneling. We find the coexistence of internal and external Josephson effects in the system, which are moreover inherently coupled in a complicated form even in the absence of interatomic interactions. Moreover, we show that the spin-dependent tunneling between two wells can induce a net atomic spin current referred as spin Josephson effects. Such novel spin Josephson effects can be observable for realistically experimental conditions.Comment: 8 page

Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin-orbit coupling in an optical lattice

We study ultracold bosonic atoms with the synthetic three-dimensional spin-orbit (SO) coupling in a cubic optical lattice. In the superfluidity phase, the lowest energy band exhibits one, two or four pairs of degenerate single-particle ground states depending on the SO-coupling strengths, which can give rise to the condensate states with spin-stripes for the weak atomic interactions. In the deep Mott-insulator regime, the effective spin Hamiltonian of the system combines three-dimensional Heisenberg exchange interactions, anisotropy interactions and Dzyaloshinskii-Moriya interactions. Based on Monte Carlo simulations, we numerically demonstrate that the resulting Hamiltonian with an additional Zeeman field has a rich phase diagram with spiral, stripe, vortex crystal, and especially Skyrmion crystal spin-textures in each xy-plane layer. The obtained Skyrmion crystals can be tunable with square and hexagonal symmetries in a columnar manner along the z axis, and moreover are stable against the inter-layer spin-spin interactions in a large parameter region.Comment: 9 pages, 4 figures; title modified, references and discussions added; accepted by PR

Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice

Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant topological metals and to physically realize them. Here we, for the first time, establish a rigorous classification of topological metals that are protected by the PT symmetry using KO-theory. As a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D Brillouin zone is constructed, whose topological stability is revealed through its PT-symmetry-protected nontrivial Z2 topological charge. Based on these exact results, we propose an experimental scheme to realize and to detect tunable PT-invariant topological NL states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent 3D OL and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. Such a realistic cold-atom setup can yield topological NL states, having a tunable ring-shaped band-touching line with the two-fold degeneracy in the bulk spectrum and non-trivial surface states. The states are actually protected by the combined PT symmetry even in the absence of both P and T symmetries, and are characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we demonstrate with numerical simulations that (i) the characteristic NL can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological NL states in cold atom systems may provide a unique experimental platform for exploring exotic PT-invariant topological physics.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.

Landau-Zener-Stuckelberg interference in a multi-anticrossing system

We propose a universal analytical method to study the dynamics of a multi-anticrossing system subject to driving by one single large-amplitude triangle pulse, within its time scales smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener-Stuckelberg interference patterns recently observed in a tripartite system [Nature Communications 1:51 (2010)]. In particular, we focus on the effects of the size of anticrossings on interference and compare the calculated interference patterns with numerical simulations. In addition, Fourier transform of the patterns can extract information on the energy level spectrum.Comment: 6 pages, 5 figure

Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms

We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to dislocation in comparison with the non-relativistic particles with the same disorder strength. More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional system for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to simulate and detect the delocalization feature of the Dirac particles with cold atoms..Comment: The version to be published in Phys. Rev. Lett.. many typos corrected; the suggested experiment was clarified

What a difference a term makes: the effect of educational attainment on marital outcomes in the UK

Abstract In the past, students in England and Wales born within the first 5 months of the academic year could leave school one term earlier than those born later in the year. Focusing on women, those who were required to stay on an extra term more frequently hold some academic qualification. Using having been required to stay on as an exogenous factor affecting academic attainment, we find that holding a low-level academic qualification has no effect on the probability of being currently married for women aged 25 or above, but increases the probability of the husband holding some academic qualification and being economically active