Entanglement and purity of single- and two-photon states

Whereas single- and two-photon wave packets are usually treated as pure states, in practice they will be mixed. We study how entanglement created with mixed photon wave packets is degraded. We find in particular that the entanglement of a delocalized single-photon state of the electro-magnetic field is determined simply by its purity. We also discuss entanglement for two-photon mixed states, as well as the influence of a vacuum component.Comment: 11 pages, 10 figures, 1 debuting autho

Exciton mediated one phonon resonant Raman scattering from one-dimensional systems

We use the Kramers-Heisenberg approach to derive a general expression for the resonant Raman scattering cross section from a one-dimensional (1D) system explicitly accounting for excitonic effects. The result should prove useful for analyzing the Raman resonance excitation profile lineshapes for a variety of 1D systems including carbon nanotubes and semiconductor quantum wires. We apply this formalism to a simple 1D model system to illustrate the similarities and differences between the free electron and correlated electron-hole theories.Comment: 10 pages, 6 figure

Environment-Mediated Quantum State Transfer

We propose a scheme for quantum state transfer(QST) between two qubits which is based on their individual interaction with a common boson environment. The corresponding single mode spin-boson Hamiltonian is solved by mapping it onto a wave propagation problem in a semi-infinite ladder and the fidelity is obtained. High fidelity occurs when the qubits are equally coupled to the boson while the fidelity becomes smaller for nonsymmetric couplings. The complete phase diagram for such an arbitrary QST mediated by bosons is discussed.Comment: 6 pages and 5 figure

Chirality dependence of the radial breathing phonon mode density in single wall carbon nanotubes

A mass and spring model is used to calculate the phonon mode dispersion for single wall carbon nanotubes (SWNTs) of arbitrary chirality. The calculated dispersions are used to determine the chirality dependence of the radial breathing phonon mode (RBM) density. Van Hove singularities, usually discussed in the context of the single particle electronic excitation spectrum, are found in the RBM density of states with distinct qualitative differences for zig zag, armchair and chiral SWNTs. The influence the phonon mode density has on the two phonon resonant Raman scattering cross-section is discussed.Comment: 6 pages, 2 figures, submitted to Phys. Rev.

Extended dual description of Mott transition beyond two-dimensional space

Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.Comment: 7 pages, no figure

Augmented L1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm

This paper studies the long-existing idea of adding a nice smooth function to "smooth" a non-differentiable objective function in the context of sparse optimization, in particular, the minimization of $||x||_1+1/(2\alpha)||x||_2^2$, where $x$ is a vector, as well as the minimization of $||X||_*+1/(2\alpha)||X||_F^2$, where $X$ is a matrix and $||X||_*$ and $||X||_F$ are the nuclear and Frobenius norms of $X$, respectively. We show that they can efficiently recover sparse vectors and low-rank matrices. In particular, they enjoy exact and stable recovery guarantees similar to those known for minimizing $||x||_1$ and $||X||_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, spherical section property, or RIPless property. To recover a (nearly) sparse vector $x^0$, minimizing $||x||_1+1/(2\alpha)||x||_2^2$ returns (nearly) the same solution as minimizing $||x||_1$ almost whenever $\alpha\ge 10||x^0||_\infty$. The same relation also holds between minimizing $||X||_*+1/(2\alpha)||X||_F^2$ and minimizing $||X||_*$ for recovering a (nearly) low-rank matrix $X^0$, if $\alpha\ge 10||X^0||_2$. Furthermore, we show that the linearized Bregman algorithm for minimizing $||x||_1+1/(2\alpha)||x||_2^2$ subject to $Ax=b$ enjoys global linear convergence as long as a nonzero solution exists, and we give an explicit rate of convergence. The convergence property does not require a solution solution or any properties on $A$. To our knowledge, this is the best known global convergence result for first-order sparse optimization algorithms.Comment: arXiv admin note: text overlap with arXiv:1207.5326 by other author

Response of internal solitary waves to tropical storm Washi in the northwestern South China Sea

Based on in-situ time series data from an array of temperature sensors and an acoustic Doppler current profiler on the continental shelf of the northwestern South China Sea, a sequence of internal solitary waves (ISWs) were observed during the passage of tropical storm Washi in the summer of 2005, which provided a unique opportunity to investigate the ISW response to the tropical cyclone. The passing tropical storm is found to play an important role in affecting the stratification structure of the water column, and consequently leading to significant variability in the propagating features of the ISWs, such as the polarity reversal and amplitude variations of the waves. The response of the ISWs to Washi can be divided into two stages, direct forcing by the strong wind (during the arrival of Washi) and remote forcing via the near-inertial internal waves induced by the tropical storm (after the passage of Washi). The field observations as well as a theoretical analysis suggest that the variations of the ISWs closely coincide with the changing stratification structure and shear currents in accompanied by the typhoon wind and near-inertial waves. This study presents the first observations and analysis of the ISW response to the tropical cyclone in the South China Sea

Tunable Resonant Raman Scattering from Singly Resonant Single Wall Carbon Nanotubes

We perform tunable resonant Raman scattering on 17 semiconducting and 7 metallic singly resonant single wall carbon nanotubes. The measured scattering cross-section as a function laser energy provides information about a tube's electronic structure, the lifetime of intermediate states involved in the scattering process and also energies of zone center optical phonons. Recording the scattered Raman signal as a function of tube location in the microscope focal plane allows us to construct two-dimensional spatial maps of singly resonant tubes. We also describe a spectral nanoscale artifact we have coined the "nano-slit effect"

Wavelet based segment detection and feature extraction for 3D T-ray CT pattern classification

Copyright © 2006 IEEEThis paper explores three dimensional (3D) Terahertz (T-rays) computed tomographic (CT) classification based on T-ray functional imaging techniques. The target objects are separated by their refractive indices, which are indicated by the intensity in the images. Segmentation techniques are employed to identify the position of each pixel belonging to the different classes. Wavelet methods are applied to the detected T-ray pulsed responses for feature extraction. A Mahalanobis distance classifier is selected for the final classification task. This paper presents T-ray CT classification techniques that allow analysis of measured T-ray transmission image statistics and that automatically identify materials within a heterogeneous structure.X.X. Yin, B.W.-H. Ng, B. Ferguson, S.P. Mickan, D. Abbot