Non-locality of non-Abelian anyons

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locality for anyonic states and it opens up the possibility to violate the Bell inequalities in quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure

From spin to anyon notation: The XXZ Heisenberg model as a D3D_{3} (or su(2)4su(2)_{4}) anyon chain

We discuss a relationship between certain one-dimensional quantum spin chains and anyon chains. In particular we show how the XXZ Heisenberg chain is realised as a $D_{3}$ (alternately $su(2)_{4}$) anyon model. We find the difference between the models lie primarily in choice of boundary condition.Comment: 13 page

GMRT mini-survey to search for 21-cm absorption in Quasar-Galaxy Pairs at z~0.1

We present the results from our 21-cm absorption survey of a sample of 5 quasar-galaxy pairs (QGPs), with the redshift of the galaxies in the range 0.03<zg<0.18, selected from the SDSS. The HI 21-cm absorption was searched towards the 9 sight lines with impact parameters ranging from 10 to 55 kpc using GMRT. 21-cm absorption was detected only in one case i.e. towards the Quasar (zq=2.625 SDSS J124157.54+633241.6)-galaxy (zg=0.143 SDSS J124157.26+633237.6) pair with the impact parameter 11 kpc. The quasar sight line in this case pierces through the stellar disk of a galaxy having near solar metallicity (i.e (O/H)+12=8.7) and star formation rate uncorrected for dust attenuation of 0.1 M_odot/yr. The quasar spectrum reddened by the foreground galaxy is well fitted with the Milky Way extinction curve (with an Av of 0.44) and the estimated HI column density is similar to the value obtained from 21-cm absorption assuming spin temperature of 100K. Combining our sample with the z<0.1 data available in the literature, we find the detectability of 21-cm absorption with integrated optical depth greater than 0.1 km\s to be 50% for the impact parameter less than 20 kpc. Using the surface brightness profiles and relationship between the optical size and extent of the HI disk known for nearby galaxies, we conclude that in most of the cases of 21-cm absorption non-detection, the sight lines may not be passing through the HI gas. We also find that in comparison to the absorption systems associated with these QGPs, z<1 DLAs with 21-cm absorption detections have lower CaII equivalent widths despite having higher 21-cm optical depths and smaller impact parameters. This suggests that the current sample of DLAs may be a biased population that avoids sight lines through dusty star-forming galaxies. A systematic survey of QGPs is needed to confirm these findings and understand the nature of 21-cm absorbers.Comment: 17 pages, 5 tables, 19 figures, accepted for publication in MNRAS (abstract abridged

Qudit surface codes and gauge theory with finite cyclic groups

Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2 (qubit) lattices, such ground states have been proposed as topologically protected memory for qubits. We extend these constructions to lattices or more generally cell complexes with qudits, either of prime level or of level $d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor decomposition, to arbitrary finite levels. The Hamiltonian describes an exact $\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations correspond to abelian anyons. We provide protocols for qudit storage and retrieval and propose an interferometric verification of topological order by measuring quasi-particle statistics.Comment: 26 pages, 5 figure

Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator

Recently a pair of experiments demonstrated a simulation of Abelian anyons in a spin network of single photons. The experiments were based on an Abelian discrete gauge theory spin lattice model of Kitaev. Here we describe how to use linear optics and single photons to simulate non-Abelian anyons. The scheme makes use of joint qutrit-qubit encoding of the spins and the resources required are three pairs of parametric down converted photons and 14 beam splitters.Comment: 13 pages, 5 figures. Several references added in v

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules

Fourier transform and the Verlinde formula for the quantum double of a finite group

A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D(G). The Fourier transform relates the two ring structures. We use this to give a particularly short proof of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to appear in Journal of Physics

Quasars probing intermediate redshift star-forming galaxies

We present a sample of 46 [OIII]-emitting galaxies at z<0.8 detected in the fibre spectra of quasars from the SDSS-DR7 through an automatic search procedure. We also detect [OII] and Hb emission lines from most of these galaxies in the SDSS spectra. We study both the emission and absorption properties of a sub-sample of 17 galaxies in the redshift range z=0.4-0.7, where MgII lines are covered by the SDSS spectra. The measured lower-limits on the star-formation rates of these galaxies are in the range 0.2-20 M_sun/yr. The emission line luminosities and (O/H) metallicities from R23 measured in this sample are similar to what is found in normal galaxies at these redshifts. Thus, this constitutes a unique sample of intermediate redshift star-forming galaxies where we can study the QSO absorber - galaxy connection. Strong MgII (W>1A) as well as MgI absorption lines are detected in the QSO spectra at the redshift of most of these galaxies. Strong FeII (W>1A) absorption lines are also generally detected whenever the appropriate wavelength ranges are covered. This suggests that most of these systems could be bona-fide Damped Lyman-alpha systems. We investigate various possible relations between the MgII rest equivalent widths and the emission line properties. We find a possible (2 sigma) correlation between the emission-line metallicity of the galaxies and the MgII rest equivalent width of the absorbers [truncated].Comment: 15 pages, 11 figures, 5 tables. accepted for publication in MNRA

Realizing non-Abelian statistics

We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of 1+1-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical two-dimensional Potts model. We discuss the transition from a topological phase to a conventionally-ordered phase, showing in some cases there is a quantum critical point.Comment: 20 pages in two-column format. v2: fixed typos and added reference

The nature of LINER galaxies: Ubiquitous hot old stars and rare accreting black holes

Galaxies, which often contain ionised gas, sometimes also exhibit a so-called low-ionisation nuclear emission line region (LINER). For 30 years this was attributed to a central mass-accreting supermassive black hole (AGN) of low luminosity, making LINER galaxies the largest AGN-sub-population, dominating in numbers over higher luminosity Seyfert galaxies and quasars. This, however, poses a serious problem. While the inferred energy balance is plausible, many LINERs clearly do not contain any other independent signatures of an AGN. Using integral field spectroscopic data from the CALIFA survey, we aim at comparing the observed radial surface brightness profiles with what is expected from illumination by an AGN. Essential for this analysis is a proper extraction of emission-lines, especially weak lines such as the Balmer Hb line which is superposed on an absorption trough. To accomplish this, we use the GANDALF code which simultaneously fits the underlying stellar continuum and emission lines. We show for 48 galaxies with LINER-like emission, that the radial emission-line surface brightness profiles are inconsistent with ionisation by a central point-source and hence cannot be due to an AGN alone. The most probable explanation for the excess LINER-like emission is ionisation by evolved stars during the short but very hot and energetic phase known as post-AGB. This leads us to an entirely new interpretation. Post-AGB stars are ubiquitous and their ionising effect should be potentially observable in every galaxy with gas present and stars older than ~1 Gyr, unless a stronger radiation field from young hot stars or an AGN outshines them. This means that galaxies with LINER-like emission are in fact not a class defined by a property, but rather by the absence of a property. It also explains why LINER emission is observed mostly in massive galaxies with old stars and little star formation.Comment: 8 pages, 7 figure