Application of cogwheel phase cycling to sideband manipulation experiments in solid-state NMR

Cogwheel phase-cycling schemes are applied to sideband suppression and sideband separation experiments in solid-state NMR. It is shown that cogwheel phase cycles lead to the elimination of most pulse imperfection effects, while using far fewer experimental signal acquisitions than conventional phase-cycling methods.     

Non-linear Sagnac interferometry for pump-probe dispersion spectroscopy

We explore pump-probe non-linear Sagnac interferometry as a tool to measure the dispersive properties of a medium. We introduce the background theory, and show experimental spectra obtained on the D₂ transition with ⁸⁵Rb and ⁸⁷Rb. The measured dispersion spectra are in excellent agreement with the Kramers-Kronig relations. In addition, as both beams traverse identical optical paths, Sagnac interferometry is very robust against mechanical vibrationReceived: 5 June 2003, Published online: 16 September 2003PACS: 39.30. + w Spectroscopic techniques - 33.55.Ad Optical activity, optical rotation; circular dichroismG. Jundt: Present address: Institute of Quantum Electronics, Department of Physics, ETH Zürich, Hönggerberg 8093, Switzerland.     

Integral kašin splittings

Forx ∈ ℝ ⁿ andp≥1 put ‖x‖ _p :=(n ⁻¹Σ|x _i| ^p )^1/p . An orthogonal direct sum decomposition ℝ^2k =E⊕E ^⊥ where dimE=k and ‖x‖₂/‖x‖₁≤C is called here a (k, C)-splitting. By a theorem of Kašin there existsC>0 such that (k, C)-splittings exist for allk, and by the volume ratio method of Szarek one can takeC=32eπ. All proofs of existence of (k, C)-splittings heretofore given are nonconstructive. Here we investigate the representation of (k, C)-splittings by matrices with integral entries. For everyC>8e _1/2 π _−1/2 and positive integerk we specify a positive integerN(k, C) such that in the set ofk by 2k matrices with integral entries of absolute value not exceedingN(k, C) there exists a matrix with row span a summand in a (k, C)-splitting. We haveN(k, C)≤2^18k fork large enough depending onC. We explain in detail how to test a matrix for the property of representing a (k, C)-splitting. Taken together our results yield an explicit (if impractical) construction of (k, C)-splittings.     

A generalization of Filliman duality

Filliman duality expresses (the characteristic measure of) a convex polytope containing the origin as an alternating sum of simplices that share supporting hyperplanes with . The terms in the alternating sum are given by a triangulation of the polar body . The duality can lead to useful formulas for the volume of . A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of .

In this note we extend Filliman duality to an involution on the space of polytopal measures on a finite-dimensional vector space, excluding polytopes that have a supporting hyperplane coplanar with the origin. As a special case, if is a convex polytope containing the origin, any realization of as a linear combination of simplices leads to a dual realization of .

     

Graded nanostructures produced by sliding and exhibiting universal behavior

Nanostructured copper was produced by deformation under large sliding loads. In the near surface layers, 10 nm scale microstructures form and coarsen with increasing depth from the surface. The graded structure enables characterization of the structural scale over several orders of magnitude. Analysis reveals that universal scaling of the microstructure exists from 10,000 to 10 nm. The limit of scale is pushed to an order of magnitude of the ultimate scale at which the crystallinity is lost. This universality opens the door for easy manufacture of ever finer scale components by deformation.     

Broadband time-domain reflectometry measurement of attenuation and phase velocity in highly attenuating suspensions with application to the ultrasound contrast medium Albunex

We describe a technique for broadband measurements of the attenuation coefficient and phase velocity of highly attenuating liquid suspensions. To validate the technique we apply it to the ultrasound contrast agent Albunex at concentrations ranging from 0.69 x 10(6) particles/mL to 364 x 10(6) particles/mL. These longitudinal wave measurements were performed on Albunex suspensions maintained at 37 degrees C in a special time-domain reflectometer designed and constructed in our laboratory. The frequency-dependent attenuation coefficients and phase velocities obtained in the reflectometer are compared to broadband through-transmission measurements of these same quantities, which were also performed in our laboratory. Although comparison data between the two techniques are only available at lower concentrations, the agreement is quite good and serves to validate the methods described in this paper.     

Transverse asymmetry AT' from the quasielastic 3He(e,e') process and the neutron magnetic form factor

We have measured the transverse asymmetry A(T') in 3He(e,e(')) quasielastic scattering in Hall A at Jefferson Laboratory with high precision for Q2 values from 0.1 to 0.6 (GeV/c)(2). The neutron magnetic form factor G(n)(M) was extracted based on Faddeev calculations for Q2 = 0.1 and 0.2 (GeV/c)(2) with an experimental uncertainty of less than 2%.     

Observation of power-Law scaling for phase transitions in linear trapped ion crystals

We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to ten ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.     

Calculation of pulsed NMR signal in I = 3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.