Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF requires exactly the same minimal storage as packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full format routine and two calls to Level 3 BLAS routines. This means {\it no} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines

Influence of optical aberrations in an atomic gyroscope

In atom interferometry based on light-induced diffraction, the optical aberrations of the laser beam splitters are a dominant source of noise and systematic effect. In an atomic gyroscope, this effect is dramatically reduced by the use of two atomic sources. But it remains critical while coupled to fluctuations of atomic trajectories, and appears as a main source of noise to the long term stability. Therefore we measure these contributions in our setup, using cold Cesium atoms and stimulated Raman transitions

The Lookup Technique to Replace Nested-IF Formulas in Spreadsheet Programming

Spreadsheet programmers often implement contingent logic using a nested-IF formula even though this technique is difficult to test and audit and is believed to be risky. We interpret the programming of contingent logic in spreadsheets in the context of traditional computer programming. We investigate the “lookup technique” as an alternative to nested-IF formulas, describe its benefits for testing and auditing, and define its limitations. The lookup technique employs four distinct principles: 1) make logical tests visible; 2) make outcomes visible; 3) make logical structure visible; and 4) replace a multi-function nested-IF formula with a single-function lookup formula. It can be used only for certain simple contingent logic. We describe how the principles can be applied in more complex situations, and suggest avenues for further research

Propagation of Bose-Einstein condensates in a magnetic waveguide

Gaseous Bose-Einstein condensates of 2-3 million atoms were loaded into a microfabricated magnetic trap using optical tweezers. Subsequently, the condensates were released into a magnetic waveguide and propagated 12 mm. Single-mode propagation was observed along homogeneous segments of the waveguide. Inhomogeneities in the guiding potential arose from geometric deformations of the microfabricated wires and caused strong transverse excitations. Such deformations may restrict the waveguide physics that can be explored with propagating condensates.Comment: 5 pages, 4 figure

Quantum-enhanced gyroscopy with rotating anisotropic Bose–Einstein condensates

High-precision gyroscopes are a key component of inertial navigation systems. By considering matter wave gyroscopes that make use of entanglement it should be possible to gain some advantages in terms of sensitivity, size, and resources used over unentangled optical systems. In this paper we consider the details of such a quantum-enhanced atom interferometry scheme based on atoms trapped in a carefully-chosen rotating trap. We consider all the steps: entanglement generation, phase imprinting, and read-out of the signal and show that quantum enhancement should be possible in principle. While the improvement in performance over equivalent unentangled schemes is small, our feasibility study opens the door to further developments and improvements

First electron beam polarization measurements with a Compton polarimeter at Jefferson Laboratory

A Compton polarimeter has been installed in Hall A at Jefferson Laboratory. This letter reports on the first electron beam polarization measurements performed during the HAPPEX experiment at an electron energy of 3.3 GeV and an average current of 40 $\mu$A. The heart of this device is a Fabry-Perot cavity which increased the luminosity for Compton scattering in the interaction region so much that a 1.4% statistical accuracy could be obtained within one hour, with a 3.3% total error

Transport of Bose-Einstein Condensates with Optical Tweezers

We have transported gaseous Bose-Einstein condensates over distances up to 44 cm. This was accomplished by trapping the condensate in the focus of an infrared laser and translating the location of the laser focus with controlled acceleration. Condensates of order 1 million atoms were moved into an auxiliary chamber and loaded into a magnetic trap formed by a Z-shaped wire. This transport technique avoids the optical and mechanical access constraints of conventional condensate experiments and creates many new scientific opportunities.Comment: 5 pages, 3 figure

Novel Ferromagnetic Atom Waveguide with in situ loading

Magneto-optic and magnetostatic trapping is realized near a surface using current carrying coils wrapped around magnetizable cores. A cloud of 10^7 Cesium atoms is created with currents less than 50 mA. Ramping up the current while maintaining optical dissipation leads to tightly confined atom clouds with an aspect ratio of 1:1000. We study the 3D character of the magnetic potential and characterize atom number and density as a function of the applied current. The field gradient in the transverse dimension has been varied from < 10 G/cm to > 1 kG/cm. By loading and cooling atoms in-situ, we have eliminated the problem of coupling from a MOT into a smaller phase space.Comment: 4 pages, 4 figure