A Corollary for Nonsmooth Systems

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function

Long-range beam-beam experiments in the relativistic heavy ion collider

Long-range beam-beam effects are a potential limit to the LHC performance with the nominal design parameters, and certain upgrade scenarios under discussion. To mitigate long-range effects, current carrying wires parallel to the beam were proposed and space is reserved in the LHC for such wires. Two current carrying wires were installed in RHIC to study the effect of strong long-range beam-beam effects in a collider, as well as test the compensation of a single long-range interaction. The experimental data were used to benchmark simulations. We summarize this work.Comment: 12 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201

Readout Concepts for DEPFET Pixel Arrays

Field effect transistors embedded into a depleted silicon bulk (DEPFETs) can be used as the first amplifying element for the detection of small signal charges deposited in the bulk by ionizing particles, X-ray photons or visible light. Very good noise performance at room temperature due to the low capacitance of the collecting electrode has been demonstrated. Regular two dimensional arrangements of DEPFETs can be read out by turning on individual rows and reading currents or voltages in the columns. Such arrangements allow the fast, low power readout of larger arrays with the possibility of random access to selected pixels. In this paper, different readout concepts are discussed as they are required for arrays with incomplete or complete clear and for readout at the source or the drain. Examples of VLSI chips for the steering of the gate and clear rows and for reading out the columns are presented.Comment: 8 pages, 9 figures, submitted to Nucl. Instr. and Methods as proceedings of the 9th European Symposium on Semiconductor Detectors, Elmau, June 23-27, 200

Existence of Long-Range Order for Trapped Interacting Bosons

We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.Comment: 4 pages, 1 figure, RevTex4. Title changed at the request of editors; to appear in Phys. Rev. Letter

Compact solid-state laser source for 1S-2S spectroscopy in atomic hydrogen

We demonstrate a novel compact solid-state laser source for high-resolution two-photon spectroscopy of the $1S-2S$ transition in atomic hydrogen. The source emits up to 20 mW at 243 nm and consists of a 972 nm diode laser, a tapered amplifier, and two doubling stages. The diode laser is actively stabilized to a high-finesse cavity. We compare the new source to the stable 486 nm dye laser used in previous experiments and record 1S-2S spectra using both systems. With the solid-state laser system we demonstrate a resolution of the hydrogen spectrometer of 6 \times 10^{11} which is promising for a number of high-precision measurements in hydrogen-like systems

Emittance growth with offset beam-beam collisions and small beam-beam parameters

N/

Six-dimensional weak-strong simulations of head-on beam-beam compensation in RHIC

To compensate the large beam-beam tune spread and beam-beam resonance driving terms in the polarized proton operation in the Relativistic Heavy Ion Collider (RHIC), we will introduce a low-energy DC electron beam into each ring to collide head-on with the opposing proton beam. The device to provide the electron beam is called an electron lens. In this article, using a 6-D weak-strong-beam-beam interaction simulation model, we investigate the effects of head-on beam-beam compensation with electron lenses on the proton beam dynamics in the RHIC 250 GeV polarized proton operation. This article is abridged from the published article [1].Comment: 5 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201

Improving broadband displacement detection with quantum correlations

Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the tradeoff between the probe's shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as \textit{variational readout}, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And more generally our result is a salient example of how correlations can aid sensing in the presence of backaction.Comment: 17 pages, 5 figure

High-Precision Optical Measurement of the 2S Hyperfine Interval in Atomic Hydrogen

We have applied an optical method to the measurement of the 2S hyperfine interval in atomic hydrogen. The interval has been measured by means of two-photon spectroscopy of the 1S-2S transition on a hydrogen atomic beam shielded from external magnetic fields. The measured value of the 2S hyperfine interval is equal to 177 556 860(15) Hz and represents the most precise measurement of this interval to date. The theoretical evaluation of the specific combination of 1S and 2S hyperfine intervals D_21 is in moderately good agreement with the value for D_21 deduced from our measurement

Probing Unquenching Effects in the Gluon Polarisation in Light Mesons

We introduce an extension to the ladder truncated Bethe-Salpeter equation for mesons and the rainbow truncated quark Dyson-Schwinger equations which includes quark-loop corrections to the gluon propagator. This truncation scheme obeys the axialvector Ward-Takahashi identity relating the quark self-energy and the Bethe-Salpeter kernel. Two different approximations to the Yang-Mills sector are used as input: the first is a sophisticated truncation of the full Yang-Mills Dyson-Schwinger equations, the second is a phenomenologically motivated form. We find that the spectra and decay constants of pseudoscalar and vector mesons are overall described well for either approach. Meson mass results for charge eigenstate vector and pseudoscalar meson masses are compared to lattice data. The effects of unquenching the system are small but not negligible.Comment: 26 pages, 13 figure