Photonic Anomalous Quantum Hall Effect

We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically non-trivial bandgap. Using direct imaging and on-chip transmission measurements, we show that the bandgap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counter-clockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. We show that the two pseudospins acquire opposite hopping phases and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing

Limit distributions for the maxima of stationary Gaussian processes

AbstractLet {Xn} be a stationary Gaussian sequence with E{X0} = 0, {X20} = 1 and E{X0Xn} = rn n Let cn = (2ln n)built12, bn = cn− 12c-1n ln(4π ln n), and set Mn = max0 ⩽k⩽nXk. A classical result for independent normal random variables is that P[cn(Mn−bn)⩽x]→exp[-e-x] as n → ∞ for all x. Berman has shown that (1) applies as well to dependent sequences provided rnlnn = o(1). Suppose now that {rn} is a convex correlation sequence satisfying rn = o(1), (rnlnn)-1 is monotone for large n and o(1). Then P[rn-12(Mn − (1−rn)12bn)⩽x] → Ф(x) for all x, where Ф is the normal distribution function. While the normal can thus be viewed as a second natural limit distribution for {Mn}, there are others. In particular, the limit distribution is given below when rn is (sufficiently close to) γ/ln n. We further exhibit a collection of limit distributions which can arise when rn decays to zero in a nonsmooth manner. Continuous parameter Gaussian processes are also considered. A modified version of (1) has been given by Pickands for some continuous processes which possess sufficient asymptotic independence properties. Under a weaker form of asymptotic independence, we obtain a version of (2)

Generating Explanatory Captions for Information Graphics

Graphical presentations can be used to communicate information in relational data sets succinctly and effectively. However, novel graphical presentations about numerous attributes and their relationships are often difficult to understand completely until explained. Automatically generated graphical presentations must therefore either be limited to simple, conventional ones, or risk incomprehensibility. One way of alleviating this problem is to design graphical presentation systems that can work in conjunction with a natural language generator to produce "explanatory captions." This paper presents three strategies for generating explanatory captions to accompany information graphics based on: (1) a representation of the structure of the graphical presentation (2) a framework for identifyingthe perceptual complexity of graphical elements, and (3) the structure of the data expressed in the graphic. We describe an implemented system and illustrate how it is used to generate explanatory cap..

Ab initio lattice dynamics simulations and inelastic neutron scattering spectra for studying phonons in BaFe2As2: Effect of structural phase transition, structural relaxation and magnetic ordering

We have performed extensive ab initio calculations to investigate phonon dynamics and their possible role in superconductivity in BaFe2As2 and related systems. The calculations are compared to inelastic neutron scattering data that offer improved resolution over published data [Mittal et al., PRB 78 104514 (2008)], in particular at low frequencies. Effects of structural phase transition and full/partial structural relaxation, with and without magnetic ordering, on the calculated vibrational density of states are reported. Phonons are best reproduced using either the relaxed magnetic structures or the experimental cell. Several phonon branches are affected by the subtle structural changes associated with the transition from the tetragonal to the orthorhombic phase. Effects of phonon induced distortions on the electronic and spin structure have been investigated. It is found that for some vibrational modes, there is a significant change of the electronic distribution and spin populations around the Fermi level. A peak at 20 meV in the experimental data falls into the pseudo-gap region of the calculation. This was also the case reported in our recent work combined with an empirical parametric calculation [Mittal et al., PRB 78 104514 (2008)]. The combined evidence for the coupling of electronic and spin degrees of freedom with phonons is relevant to the current interest in superconductivity in BaFe2As2 and related systems