Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Studies of molecular bonding, interactions and decomposition reactions on the (001) surface of ruthenium

The interactions of N₂, formic acid and acetone on the Ru(001) surface are studied using thermal desorption mass spectrometry (TDMS), electron energy loss spectroscopy (EELS), and computer modeling.

Low energy electron diffraction (LEED), EELS and TDMS were used to study chemisorption of N₂ on Ru(001). Adsorption at 75 K produces two desorption states. Adsorption at 95 K fills only the higher energy desorption state and produces a (√3 x √3)R30° LEED pattern. EEL spectra indicate both desorption states are populated by N₂ molecules bonded "on-top" of Ru atoms.

Monte Carlo simulation results are presented on Ru(001) using a kinetic lattice gas model with precursor mediated adsorption, desorption and migration. The model gives good agreement with experimental data. The island growth rate was computed using the same model and is well fit by R(t)^m - R(t₀)^m = At, with m approximately 8. The island size was determined from the width of the superlattice diffraction feature.

The techniques, algorithms and computer programs used for simulations are documented. Coordinate schemes for indexing sites on a 2-D hexagonal lattice, programs for simulation of adsorption and desorption, techniques for analysis of ordering, and computer graphics routines are discussed.

The adsorption of formic acid on Ru(001) has been studied by EELS and TDMS. Large exposures produce a molecular multilayer species. A monodentate formate, bidentate formate, and a hydroxyl species are stable intermediates in formic acid decomposition. The monodentate formate species is converted to the bidentate species by heating. Formic acid decomposition products are CO₂, CO, H₂, H₂O and oxygen adatoms. The ratio of desorbed CO with respect to CO₂ increases both with slower heating rates and with lower coverages.

The existence of two different forms of adsorbed acetone, side-on, bonded through the oxygen and acyl carbon, and end-on, bonded through the oxygen, have been verified by EELS. On Pt(111), only the end-on species is observed. On dean Ru(001) and p(2 x 2)O precovered Ru(001), both forms coexist. The side-on species is dominant on clean Ru(001), while O stabilizes the end-on form. The end-on form desorbs molecularly. Bonding geometry stability is explained by surface Lewis acidity and by comparison to organometallic coordination complexes.

Femtosecond laser-induced ZnSe nanowires on the surface of a ZnSe wafer in water

We present a simple route for ZnSe nanowire growth in the ablation crater on a ZnSe crystal surface. The crystal wafer, which was horizontally dipped in pure water, was irradiated by femtosecond laser pulses. No furnace, vacuum chamber or any metal catalyst were used in this experiment. The size of the nanowires is about 1-3 mu m long and 50-150 nm in diameter. The growth rate is 1-3 mu m/s, which is much higher than that achieved with molecular-beam epitaxy and chemical vapor deposition methods. Our discovery reveals a rapid and simple way to grow nanowires on designed micro-patterns, which may have potential applications in microscopic optoelectronics. (C) 2007 Elsevier Ltd. All rights reserved.

Electronic states in disordered topological insulators

We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi₂Se₃ and Bi₂Te₃ exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green's function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.

Quantum Interference and Entanglement of Surface Plasmons

Surface plasma waves arise from the collective oscillations of billions of electrons at the surface of a metal in unison. The simplest way to quantize these waves is by direct analogy to electromagnetic fields in free space, with the surface plasmon, the quantum of the surface plasma wave, playing the same role as the photon. It follows that surface plasmons should exhibit all of the same quantum phenomena that photons do, including quantum interference and entanglement.

Unlike photons, however, surface plasmons suffer strong losses that arise from the scattering of free electrons from other electrons, phonons, and surfaces. Under some circumstances, these interactions might also cause “pure dephasing,” which entails a loss of coherence without absorption. Quantum descriptions of plasmons usually do not account for these effects explicitly, and sometimes ignore them altogether. In light of this extra microscopic complexity, it is necessary for experiments to test quantum models of surface plasmons.

In this thesis, I describe two such tests that my collaborators and I performed. The first was a plasmonic version of the Hong-Ou-Mandel experiment, in which we observed two-particle quantum interference between plasmons with a visibility of 93 ± 1%. This measurement confirms that surface plasmons faithfully reproduce this effect with the same visibility and mutual coherence time, to within measurement error, as in the photonic case.

The second experiment demonstrated path entanglement between surface plasmons with a visibility of 95 ± 2%, confirming that a path-entangled state can indeed survive without measurable decoherence. This measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing must have been weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.

These two experiments add quantum interference and path entanglement to a growing list of quantum phenomena that surface plasmons appear to exhibit just as clearly as photons, confirming the predictions of the simplest quantum models.

Hydrobiological service for observations and control of surface waters in the USSR

Technological progress, having reached in our time an unprecedented speed, is still increasing the rate of mineral extraction, industrial construction, and the mastering of new kinds of energy is growing. Correspondingly the anthropogenic load on the biosphere is increased and that requires the comprehensive development of monitoring the anthropogenic changes in the natural environment. Among problems resulting from the scientific-technological development, a noticeable place is given to the problem of pure water. Surface land waters proved to be a sensitive link in the natural environment. The hydrobiological service for observations and control of the surface waters is one of the subsystems of the State/Federal Service for Observations and Control of pollution levels in environmental objects, conducted by the USSR State Committee for Hydrometeor- ology and Control of the Natural Environment. This paper summarises the the main principles of the organisation and goals of the national system of monitoring of the state of the natural environment in the USSR.

Quantum ricochets: surface capture, release and energy loss of fast ions hitting a polar surface at grazing incidence

A diffraction mechanism is proposed for the capture, multiple bouncing and final escape of a fast ion (keV) impinging on the surface of a polarizable material at grazing incidence. Capture and escape are effected by elastic quantum diffraction consisting of the exchange of a parallel surface wave vector G= 2p/ a between the ion parallel momentum and the surface periodic potential of period a. Diffraction- assisted capture becomes possible for glancing angles F smaller than a critical value given by Fc 2- 2./ a-| Vim|/ E, where E is the kinetic energy of the ion,. = h/ Mv its de Broglie wavelength and Vim its average electronic image potential at the distance from the surface where diffraction takes place. For F< Fc, the ion can fall into a selected capture state in the quasi- continuous spectrum of its image potential and execute one or several ricochets before being released by the time reversed diffraction process. The capture, ricochet and escape are accompanied by a large, periodic energy loss of several tens of eV in the forward motion caused by the coherent emission of a giant number of quanta h. of Fuchs- Kliewer surface phonons characteristic of the polar material. An analytical calculation of the energy loss spectrum, based on the proposed diffraction process and using a model ion-phonon coupling developed earlier (Lucas et al 2013 J. Phys.: Condens. Matter 25 355009), is presented, which fully explains the experimental spectrum of Villette et al (2000 Phys. Rev. Lett. 85 3137) for Ne+ ions ricocheting on a LiF(001) surface.

Solid-state NMR study of bioactive binary borosilicate glasses

A series of binary borosilicate glasses prepared by the sol-gel method are shown to be bioactive. Tetraethyl orthosilicate (TEOS) and trimethylborate (TMB) in acidic medium are used to prepare xB(2)O(3)center dot(1-x)SiO2 glass systems for x = 0.045-0.167. The formation of a layer of apatite-like mineral on the glass surface becomes apparent after soaking in simulated body fluid for 48 h. We have measured the B-11-B-11 homonuclear second moments of the borosilicate glasses and inferred that no macroscopic phase separation occurred in our glasses. The B-11 chemical shift data also show that the formation of clustered boroxol rings is negligible in our glass system. Although the bioactivity of our borosilicate glasses is less than that of CaO-SiO2 sol-gel glasses, these simple binary systems could be taken as reference glass systems for the search of new bioactive borosilicate glasses. (C) 2008 Elsevier Ltd. All rights reserved.

The abiotic ecology of breeding ground of Palaemonid prawns in the Ilaje Estuary, Ondo State, Nigeria

In situ ecological assessment of the breeding grounds of palaemonid prawns was conducted in some selected locations around Ondo state coastal area between the months of April and September. Data obtained were subjected to both descriptive and inferential statistics. Three species of Palaemonid prawns were identified in four different locations within the study area with relative abundance ratio of 4:3:1. Macrobrachium macrobrachion, Nematopalaemon hastatus and Palaemon maculatus respectively. Sex ratio of 1 male to 5 females for M. macrobrachion, and 1 male to 2 females for N. hastatus and P. maculatus were observed with result showing significant relationships (P < 0.05) in distribution patterns across collection sites. Population distribution within the water column showed that palaemons are sub-lithoral prawns inhabiting maximum mean depth of 0.67m ± 0.025. Surface macro-phytes such as Eichhornia crassipies, Paspalum vaginatum, and Pistia stratiotes are common providing hiding spots for the prawn at the breeding ground. The mean soil pH across the sites stands at 6.67± 0.399 with the soil textural class that range from silty-loam to silty-clay. Also, the water quality parameters of study areas suggest that captive culture and rearing of Palaemons may be feasible outside the breeding areas.

Effect of surface plasmon resonance in TiO2/Au thin films on the fluorescence of self-assembled CdTe QDs structure

23rd Congress of the International Comission for Optics (ICO 23)

Post-processing of vertical-cavity surface-emitting lasers for transverse mode and polarization control

The operation on how high quality single-mode operation can be readily attained on etching circles in multimode devices is discussed. Arrays of such spots can also be envisaged. Control of the polarization state is also achieved by use of deep line etches. The output filaments and beam shapes of the conventional multimode vertical cavity surface emitting lasers (VCSEL) is shown to be engineered in terms of their positions, widths, and polarizations by use of focused ion beam etching (FIBE). Several GaAs quantum well top-emitting devices with cavity diameters of 10 μm and 18 μm were investigated.

Coupling between elytra of some beetles: Mechanism, forces and effect of surface texture

Lightweight materials, structures and coupling mechanisms are very important for realizing advanced flight vehicles. Here, we obtained the geometric structures and morphologies of the elytra of beetles and ascertained its coupling zone by using the histological section technique and SEM. We set up a three-dimensional motion observing system to monitor the opening and closing behaviour of elytra in beetles and to determine the motion mechanism. We constructed a force measuring system to measure the coupling forces between elytra. The results show that elytra open and close by rotating about a single axle, where the coupling forces may be as high as 160 times its own bodyweight, the elytra coupling with the tenon and mortise mechanism, surface texture and opening angle between elytra heavily influence the coupling forces. These results may provide insights into the design mechanism and structure for future vehicles of flight.