Bootstrap tomography of high-precision pulses for quantum control

Long-time dynamical decoupling and quantum control of qubits require high-precision control pulses. Full characterization (quantum tomography) of imperfect pulses presents a bootstrap problem: tomography requires initial states of a qubit which can not be prepared without imperfect pulses. We present a protocol for pulse error analysis, specifically tailored for a wide range of the single solid-state electron spins. Using a single electron spin of a nitrogen-vacancy (NV) center in diamond, we experimentally verify the correctness of the protocol, and demonstrate its usefulness for quantum control tasks

Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $\xi \to 0$ of the renormalizable R$_{\xi}$-gauge. We consider perturbation theory to one-loop order in the R$_{\xi}$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $\xi \to 0$ of the R$_{\xi}$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.Comment: 15 pages, LaTeX2e, uses the feynmf package, formulations correcte

Underestimation of Visual Texture Slant by Human Observers: A Model

The perspective image of an obliquely inclined textured surface exhibits shape and density distortions of texture elements which allow a human observer to estimate the inclination angle of the surface. However, since the work of Gibson (1950) it has been known that, in the absence of other cues, humans tend to underestimate the slant angle of the surface, particularly when the texture is perceived as being irregular. The perspective distortions which affect texture elements also shift the projected spatial frequencies of the texture in systematic ways. Using a suitable local spectral filter to measure these frequency gradients, the inclination angle of the surface may be estimated. A computational model has been developed which performs this task using distributions of outputs from filters found to be a good description of simple cell receptive fields. However, for irregular textures the filter output distributions are more like those of regular textures at shallower angles of slant, leading the computational algorithm to underestimate the slant angle. This behavioral similarity between human and algorithm suggests the possibility that a similar visual computation is performed in cortex

Estimation of Textured Surface Inclination by Parallel Local Spectral Analysis

When an inclined, uniformly textured surface is viewed by an observer or imaged by a camera, the systematic distortions of the perspective transformation will induce a predictable distribution of shifts in the projected spatial frequencies which compose the texture. By measuring these shifts using a set of filters having suitable spatial, frequency, and orientation resolution, the inclination angles of the original textured surface may be estimated. An algorithm is presented which uses the amplitude distributions of 2D Gabor filters to perform such a calculation. Central to the algorithm is a pair of iteratively executed routines. The fist adjusts local sets of parameters to reduce the error between predicted and measured filter amplitudes. The second propagates the local parameters to neighboring regions to consolidate the estimates of inclination. The algorithm is capable of operating in parallel on any number of regions in the image and with a diverse set of filter inputs

Anisotropy of the Cosmic Neutrino Background

The cosmic neutrino background (CNB) consists of low-energy relic neutrinos which decoupled from the cosmological fluid at a redshift z ~ 10^{10}. Despite being the second-most abundant particles in the universe, direct observation remains a distant challenge. Based on the measured neutrino mass differences, one species of neutrinos may still be relativistic with a thermal distribution characterized by the temperature T ~ 1.9K. We show that the temperature distribution on the sky is anisotropic, much like the photon background, experiencing Sachs-Wolfe and integrated Sachs-Wolfe effects.Comment: 5 pages, 2 figures / updated references, discussion of earlier wor

Receptive Fields for the Determination of Textured Surface Inclination

The image of a uniformly textured inclined surface exhibits systematic distortions which affect the projection of the spatial frequencies of which the texture is composed. Using a set of filters having suitable spatial, frequency and orientation resolution, the inclination angle of the textured surface may be estimated from the resulting spatial frequency gradients. Psychophysical experiments suggest that, in absence of other cues, humans perceive surface inclination from perspective distortions, suggesting the possibility of a specific neuronal mechanism in the visual system. Beginning with a low level filter model found to be an accurate and economical model for simple cell receptive fields, we have developed both algorithmic machine vision and neural network models to investigate physiologically plausible mechanisms for this behavior. The two models are related through a new class of receptive field formed in the hidden layer of a neural network which learned to solve the problem. This receptive field can also be described analytically from the analysis developed for the algorithmic study. This paper, then, offers a prediction for a new type of receptive field in cortex which may be involved in the perception of inclined textured surfaces

Communications Biophysics

Contains reports on three research projects.United States Air Force (Contract AF19(604)-4112

Standard Model Neutrinos as Warm Dark Matter

Standard Model neutrinos are not usually considered plausible dark matter candidates because the usual treatment of their decoupling in the early universe implies that their mass must be sufficiently small to make them ``hot'' dark matter. In this paper we show that decoupling of Standard Model neutrinos in low reheat models may result in neutrino densities very much less than usually assumed, and thus their mass may be in the keV range. Standard Model neutrinos may therefore be warm dark matter candidates.Comment: 5 pages, 5 figures, LaTeX file uses revtex packag

First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations

Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is expressed as infinite series of integrals over joint probability densities of $x$ and its velocity $\dot{x}$. Approximating higher order terms of this series through the lower order ones leads to closed expressions in the cases of vanishing and moderate correlations between subsequent crossings of $x_b$. For a linear oscillator driven by white or coloured Gaussian noise, which models a resonant neuron, we show that these approximations reproduce the complex structures of the first passage time densities characteristic for the underdamped dynamics, where Markovian approximations (giving monotonous first passage time distribution) fail