Exotic phase diagram of a topological quantum system

We study the quantum phase transitions (QPTs) in the Kitaev spin model on a triangle-honeycomb lattice. In addition to the ordinary topological QPTs between Abelian and non-Abelian phases, we find new QPTs which can occur between two phases belonging to the same topological class, namely, either two non-Abelian phases with the same Chern number or two Abelian phases with the same Chern number. Such QPTs result from the singular behaviors of the nonlocal spin-spin correlation functions at the critical points.Comment: 10 pages, 5 figure

Quantum logical gates with four-level SQUIDs coupled to a superconducting resonator

We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.Comment: 6 pages, 3 figure

Dependence of the decoherence of polarization states in phase-damping channels on the frequency spectrum envelope of photons

We consider the decoherence of photons suffering in phase-damping channels. By exploring the evolutions of single-photon polarization states and two-photon polarization-entangled states, we find that different frequency spectrum envelopes of photons induce different decoherence processes. A white frequency spectrum can lead the decoherence to an ideal Markovian process. Some color frequency spectrums can induce asymptotical decoherence, while, some other color frequency spectrums can make coherence vanish periodically with variable revival amplitudes. These behaviors result from the non-Markovian effects on the decoherence process, which may give rise to a revival of coherence after complete decoherence.Comment: 7 pages, 4 figures, new results added, replaced by accepted versio

Nanoplasmonics beyond Ohm's law

In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behavior with important consequences for e.g. field-enhancement and extinction cross sections. We report on our most recent developments of a real-space formulation of an equation-of-motion that goes beyond the common local-response approximation and use of Ohm's law as the central constitutive equation. The electron gas is treated within a semi-classical hydrodynamic model with the emergence of a new intrinsic length scale. We briefly review the new governing wave equations and give examples of applying the nonlocal framework to calculation of extinction cross sections and field enhancement in isolated particles, dimers, and corrugated surfaces.Comment: Invited paper for TaCoNa-Photonics 2012 (www.tacona-photonics.org), to appear in AIP Conf. Pro

Magneto-optical properties of Co/ZnO multilayer films

Multilayer films of ZnO with Co were deposited on glass substrates then annealed in a vacuum. The magnetisation of the films increased with annealing but not the magnitude of the magneto-optical signals. The dielectric functions for the films were calculated using the MCD spectra. A Maxwell Garnett theory of a metallic Co/ZnO mixture is presented. The extent to which this explains the MCD spectra taken on the films is discussed.Comment: This paper was presented at ICM (2009) and is accepted in this form for the proceeding

A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains

We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for any choice of RBF, to linear systems in which the matrices possess block circulant structures. These linear systems can be solved efficiently using matrix decomposition algorithms and fast Fourier transforms. A suitable value for the shape parameter in the various RBFs used is found using the leave-one-out cross validation algorithm. In particular, we consider problems governed by the Poisson equation, the inhomogeneous biharmonic equation and the inhomogeneous Cauchy–Navier equations of elasticity. In addition to its simplicity, the proposed method can both achieve high accuracy and solve large-scale problems. The feasibility of the proposed techniques is illustrated by several numerical examples

Standard model plethystics

We study the vacuum geometry prescribed by the gauge invariant operators of the minimal supersymmetric standard model via the plethystic program. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which we extract the Hilbert series, encoding the invariants of the geometry at all degrees. The fully refined Hilbert series is presented as the explicit sum of 1422 rational functions. We found a good choice of weights to unrefine the Hilbert series into a rational function of a single variable, from which we can read off the dimension and the degree of the vacuum moduli space of the minimal supersymmetric standard model gauge invariants. All data in Mathematica format are also presented