Trapped-ion quantum simulator: experimental application to nonlinear interferometers

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).     

Excitation of the T> components of the giant dipole states in N > Z nuclei by muon capture

Muon capture on N > Z nuclei is proposed as a means of studying the T_> isospin component of giant dipole states. Calculations for nickel isotopes (except ⁵⁶Ni) indicate that these states are strongly excited by muon capture. Possible experiments to detect these states are discussed.     

On the algebraic formulation of collective models. I. The mass quadrupole collective model

This paper is the first in a series of three which together present a microscopic formulation of the Bohr-Mottelson (BM) collective model of the nucleus. In this article the mass quadrupole collective (MQC) model is defined and shown to be a generalization of the BM model. The MQC model eliminates the small oscillation assumption of BM and also yields the rotational and CM(3) submodels by holonomic constraints on the MQC configuration space. In addition, the MQC model is demonstrated to be an algebraic model, so that the state space of the MQC model carries an irrep of a Lie algebra of microscopic observables, the MQC algebra. An infinite class of new collective models is then given by the various inequivalent irreps of this algebra. A microscopic embedding of the BM model is achieved by decomposing the representation of the MQC algebra on many-particle state space into its irreducible components. In the second paper this decomposition is studied in detail. The third paper presents the symplectic model, which provides the realization of the collective model in the harmonic oscillator shell model.     

Collision dynamics of excited NaK. I. Reactive KNaK and elastic HeNaK collisions

The collision dynamics of excited NaK have been studied using the technique of circularly polarised laser fluorescence. A very unusual m-dependent rate is observed for KNaK* reactive or quenching collisions which is different depending on whether the initial excitation is via Q or P, R transitions. A model is presented attributing this to the spatial distribution of the ¹Π Λ-doublet components and the influence of the nuclear function. Elastic HeNaK collisions are observed and a reorientation cross section for f = 30 was evaluated. This was found to have an upper limit of 0.3 Ų. Comparison of this with HeLi₂ reorientation cross sections indicate that the presence of a permanent dipole moment has little effect on the reorientation rate in rare gas-alkali dimer collisions.     

New Triterpenes from the Bark of Western White Pine (Pinus monticola DOUGL.)

Eleven new triterpenes with the lanostene-type skeleton were isolated from the benzene extract of western white pine bark. Their structures were determined mainly on the basis of physical and spectral data.     

Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle

Using a single, harmonically trapped 9Be(+) ion, we experimentally demonstrate a technique for generation of arbitrary states of a two-level particle confined by a harmonic potential. Rather than engineering a single Hamiltonian that evolves the system to a desired final state, we implement a technique that applies a sequence of simple operations to synthesize the state.     

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

One of the most famous episodes in the early history of general relativity involves the "race" in November 1915 between Albert Einstein and David Hilbert to uncover the "correct" form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Göttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Göttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.