A detector of small harmonic displacements based on two coupled microwave cavities

The design and test of a detector of small harmonic displacements is presented. The detector is based on the principle of the parametric conversion of power between the resonant modes of two superconducting coupled microwave cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso and Radicati, who, in 1978, suggested that superconducting coupled cavities could be used as sensitive detectors of gravitational waves, and on the work of Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind. They showed that an harmonic modulation of the cavity length l produced an energy transfer between two modes of the cavity, provided that the frequency of the modulation was equal to the frequency difference of the two modes. They achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}. We repeated the Reece, Reiner and Melissinos experiment, and with an improved experimental configuration and better cavity quality, increased the sensitivity to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device are discussed and the experimental technique is explained in detail. Possible future developments, aiming at gravitational waves detection, are also outlined.Comment: 28 pages, 12 eps figures, ReVteX. \tightenlines command added to reduce number of pages. The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://link.aip.org/link/?rs

The rf control and detection system for PACO the parametric converter detector

In this technical note the rf control and detection system for a detector of small harmonic displacements based on two coupled microwave cavities (PACO) is presented. The basic idea underlying this detector is the principle of parametric power conversion between two resonant modes of the system, stimulated by the (small) harmonic modulation of one system parameter. In this experiment we change the cavity length applying an harmonic voltage to a piezo-electric crystal. The system can achieve a great sensitivity to small harmonic displacements and can be an interesting candidate for the detection of small, mechanically coupled, interactions (e.g. high frequency gravitational waves).Comment: 13 pages, 4 postscript figure

Parametric gravity wave detector

Since 1978 superconducting coupled cavities have been proposed as a sensitive detector of gravitational waves. The interaction of the gravitational wave with the cavity walls, and the esulting motion, induces the transition of some energy from an initially excited cavity mode to an empty one. The energy transfer is maximum when the frequency of the wave is equal to the frequency difference of the two cavity modes. In 1984 Reece, Reiner and Melissinos built a detector of the type proposed, and used it as a transducer of harmonic mechanical motion, achieving a sensitivity to fractional deformations of the order dx/x ~ 10^(-18). In this paper the working principles of the detector are discussed and the last experimental results summarized. New ideas for the development of a realistic gravitational waves detector are considered; the outline of a possible detector design and its expected sensitivity are also shown.Comment: 9 pages, 6 figures. Talk given at the Workshop on Electromagnetic Probes of Fundamentals Physics, Erice (Italy), October 200

A detector of gravitational waves based on coupled microwave cavities

Since 1978 superconducting coupled cavities have been proposed as sensitive detector of gravitational waves. The interaction of the gravitational wave with the cavity walls, and the resulting motion, induces the transition of some electromagnetic energy from an initially excited cavity mode to an empty one. The energy transfer is maximum when the frequency of the wave is equal to the frequency difference of the two cavity modes. In this paper the basic principles of the detector are discussed. The interaction of a gravitational wave with the cavity walls is studied in the proper reference frame of the detector, and the coupling between two electromagnetic normal modes induced by the wall motion is analyzed in detail. Noise sources are also considered; in particular the noise coming from the brownian motion of the cavity walls is analyzed. Some ideas for the developement of a realistic detector of gravitational waves are discussed; the outline of a possible detector design and its expected sensitivity are also shown.Comment: 29 pages, 12 eps figures. Typeset by REVTe

Two Coupled Superconducting Cavities as a Gravitational Wave Detector: First Experimental Results

First experimental results of a feasibility study of a gravitational wave detector based on two coupled superconducting cavities are presented. Basic physical principles underlying the detector behaviour and sensitivity limits are discussed. The detector layout is described in detail and its rf properties are showed. The limit sensitivity to small harmonic displacements at the detection frequency (around 1 MHz) is showed. The system performance as a potential g.w. detector is discussed and future developments are foreseen.Comment: 7 pages, 3 figures. Presented at the 9th Workshop on RF Superconductivity, November 1-5, 1999, Santa Fe, New Mexico, US

Chiral symmetry and the axial nucleon to Delta(1232) transition form factors

We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.Comment: 18 pages, 3 figure

Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks

We present results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios in the presence of two flavors of light sea quarks ($N_f=2$). We use Wilson light valence quarks and Wilson and static heavy valence quarks; the sea quarks are simulated with staggered fermions. Additional quenched simulations with nonperturbatively improved clover fermions allow us to improve our control of the continuum extrapolation. For our central values the masses of the sea quarks are not extrapolated to the physical $u$, $d$ masses; that is, the central values are "partially quenched." A calculation using "fat-link clover" valence fermions is also discussed but is not included in our final results. We find, for example, $f_B = 190 (7) (^{+24}_{-17}) (^{+11}_{-2}) (^{+8}_{-0})$ MeV, $f_{B_s}/f_B = 1.16 (1) (2) (2) (^{+4}_{-0})$, $f_{D_s} = 241 (5) (^{+27}_{-26}) (^{+9}_{-4}) (^{+5}_{-0})$ MeV, and $f_{B}/f_{D_s} = 0.79 (2) (^{+5}_{-4}) (3) (^{+5}_{-0})$, where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched $N_f=2$ approximation, the error due to the missing strange sea quark and to partial quenching, and an estimate of the effects of chiral logarithms at small quark mass. The last error, though quite significant in decay constant ratios, appears to be smaller than has been recently suggested by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other lattice computations to date, the lattice $u,d$ quark masses are not very light and chiral log effects may not be fully under control.Comment: Revised version includes an attempt to estimate the effects of chiral logarithms at small quark mass; central values are unchanged but one more systematic error has been added. Sections III E and V D are completely new; some changes for clarity have also been made elsewhere. 82 pages; 32 figure

Implications of an arithmetical symmetry of the commutant for modular invariants

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3)_k, we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants.Comment: 17 pages, plain TeX, DIAS-STP-92-2

More evidence of localization in the low-lying Dirac spectrum

We have extended our computation of the inverse participation ratio of low-lying (asqtad) Dirac eigenvectors in quenched SU(3). The scaling dimension of the confining manifold is clearer and very near 3. We have also computed the 2-point correlator which further characterizes the localization.Comment: presented at Lattice2005(Topology and Confinement), Dublin, July 25-30, 2005, 6 pages, 3 figures, to appear in Proceedings of Scienc

Asymptotic scaling of the gluon propagtor on the lattice

We pursue the study of the high energy behaviour of the gluon propagator on the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in a precedin g paper that the gluon propagator did not reach three-loop asymptotic scaling at an energy scale as high as 5 GeV. Our present high statistics analysis includes also a simulation at $\beta=6.8$ ($a\simeq 0.03$ fm), which allows to reach $\mu \simeq 10$ GeV. Special care has been devoted to the finite lattice-spacing artifacts as well as to the finite volume effects, the latter being acute at $\beta=6.8$ where the volume is bounded by technical limits. Our main conclusion is a strong evidence that the gluon propagator has reached three-loop asymptotic scaling, at $\mu$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on several demanding criteria of asymptoticity, including scheme independence. Our fit in the 5.6 GeV to 9.5 GeV window yields $\Lambda^{\bar{{\rm MS}}} = 319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result, $\Lambda^{\bar{{\rm MS}}} = 295 \pm 20$ MeV, obtained from the three gluon vertex, but it is significantly above the Schr\"odinger functional method estimate : $238 \pm 19$ MeV. The latter difference is not understood. Confirming our previous paper, we show that a fourth loop is necessary to fit the whole ($2.8 \div 9.5$) GeV energy window.Comment: latex-file, 19 pgs., 6 fig