Hierarchical Wigner Crystal at the Edge of Quantum Hall Bar

We show that quasiholes persist near the edge of incompressible Quantum Hall state forming a Wigner structure. The average density of quasiholes is fixed by electrostatics and decreases slowly with increasing distance from the edge. As we see from elementary reasoning, their specific arrangement can not be a regular Wigner lattice and shows a complex hierarchical structure of dislocations.Comment: LaTEX file. Ps figures upon reques

Optimal Axes of Siberian Snakes for Polarized Proton Acceleration

Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies. First-order resonance effects can be avoided by installing Siberian Snakes in the ring, devices which rotate the spin by 180 degrees around the snake axis while not changing the beam's orbit significantly. For large rings, several Siberian Snakes are required. Here a criterion will be derived that allows to find an optimal choice of the snake axes. Rings with super-period four are analyzed in detail, and the HERA proton ring is used as an example for approximate four-fold symmetry. The proposed arrangement of Siberian Snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snakes matching. It will be shown that in general at least eight Siberian Snakes are needed and that there are exactly four possibilities to arrange their axes. When the betatron phase advance between snakes is chosen suitably, four Siberian Snakes can be sufficient. To show that favorable choice of snakes have been found, polarized protons are tracked for part of HERA-p's acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian Snakes.Comment: 14 pages, 16 figure

Magnetic field-induced spectroscopy of forbidden optical transitions with application to lattice-based optical atomic clocks

We develop a method of spectroscopy that uses a weak static magnetic field to enable direct optical excitation of forbidden electric-dipole transitions that are otherwise prohibitively weak. The power of this scheme is demonstrated using the important application of optical atomic clocks based on neutral atoms confined to an optical lattice. The simple experimental implementation of this method -- a single clock laser combined with a DC magnetic field-- relaxes stringent requirements in current lattice-based clocks (e.g., magnetic field shielding and light polarization), and could therefore expedite the realization of the extraordinary performance level predicted for these clocks. We estimate that a clock using alkaline earth-like atoms such as Yb could achieve a fractional frequency uncertainty of well below 10^-17 for the metrologically preferred even isotopes

A Study of an Inverted Wing with Endplates in Ground Effect

The aerodynamics of an inverted wing with endplates in ground effect has been investigated using experimental methods. A wind tunnel containing a moving belt was used to reproduce the effect of the ground on the flow field and the measurements were made using Laser Doppler Anemometry (LDA). Flow visualization showed that the implementation of an endplate on a wing yields the formation of two corotating vortices originating from the top and the bottom of the endplate. Initially the effect of the size of the endplate and the height of the wing above the ground on the vortices behaviour was studied. Then, the most relevant configuration of the wing was studied using LDA measurements

Phase structure and monopoles in U(1) gauge theory

We investigate the phase structure of pure compact U(1) lattice gauge theory in 4 dimensions with the Wilson action supplemented by a monopole term. To overcome the suppression of transitions between the phases in the simulations we make the monopole coupling a dynamical variable. We determine the phase diagram and find that the strength of the first order transition decreases with increasing weight of the monopole term, the transition thus ultimately getting of second order. After outlining the appropriate topological characterization of networks of currents lines, we present an analysis of the occurring monopole currents which shows that the phases are related to topological properties.Comment: 22 pages (latex), 14 figures (available upon request), BU-HEP 94-

Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

Scaling of geometric phases close to quantum phase transition in the XY chain

We show that geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that geometric phase is non-analytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, universality in the critical properties of the geometric phase in a family of models is verified. In addition, since quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by Berry curvature, the established relation between geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.Comment: 4 page

Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice

We report direct single-laser excitation of the strictly forbidden (6s^2)^1S_0 -(6s6p)^3P_0 clock transition in the even 174Yb isotope confined to a 1D optical lattice. A small (~1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FHWM) with high contrast were observed, demonstrating a record neutral-atom resonance quality factor of 2.6x10^13. The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35+/-0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks, and can create new clock possibilities in other alkaline earth-like atoms such as Mg and Ca.Comment: Submitted to Physics Review Letter