M. Cerdonio

Thermal magnetic noise in rf SQUIDS coupled to ferromagnetic cores

We present a simple model for the thermal magnetic noise in a rf SQUID coupled to a ferromagnetic core via a superconducting dc flux transformer. We show that, under conditions that are almost always fulfilled in practice, the coupling to the core can be described in terms of a SQUID frequency‐dependent complex inductance Ls (ω). This inductance reduces to an ordinary, frequency‐independent real value above a roll‐off frequency ωc . To this inductance, a Nyquist flux noise generator is associated, with spectral density S’2φi(ω) =−4kBT Im[Ls(ω)]/ ω, where kB is the Boltzmann constant, T the temperature, and Im[Ls (ω)] the imaginary part of Ls (ω). If ωc ≪ωrf , with ωrf the frequency of the rf pump, then the response of the SQUID to low‐frequency signals is not modified by the coupling to the core, while the above Nyquist noise acts as an additive input noise. We experimentally demonstrate the model for a SQUID coupled to a toroidal core.

Experimental measurement of the dynamic photothermal effect in Fabry-Perot cavities for gravitational wave detectors

We report the experimental observation of the photothermal effect. The measurements are performed by modulating the laser power absorbed by the mirrors of two high-finesse Fabry-Perot cavities. The results are very well described by a recently proposed theoretical model [M. Cerdonio, L. Conti, A. Heidmann and M. Pinard, Phys. Rev. D 63 (2001) 082003], confirming the correctness of such calculations. Our observations and quantitative characterization of the photothermal effect demonstrate its critical importance for high sensitivity interferometric displacement measurements, as those necessary for gravitational wave detection.

Thermal magnetization noise as a function of frequency in amorphous ferromagnets

We report the observation of 1/frequency magnetization noise in toroidal strip‐wound cores of amorphous ferromagnetic alloys at liquid‐helium temperatures and in the frequency range 0.1 Hz–1 kHz. The materials tested are Co‐based alloys, and exhibit very low magnetostriction and good soft magnetic properties. The experimental apparatus consists of a radio frequency SQUID magnetometer coupled to the sample by a superconducting flux transformer which is devised to allow measurements of its complex inductance. We show that the magnetization noise obeys in detail the fluctuation‐dissipation theorem. A temperature‐dependent partial roll‐off of the complex permeability is found at ∼100 Hz, possibly linked to pinning wells for domain‐wall motion. The link between 1/frequency noise and magnetic viscosity is briefly discussed.

Dragging of inertial frames by the rotating Earth: Proposal and feasibility for a ground-based detection

We are proposing a ground-based experiment to detect the Lense-Thirring drag due to the rotating earth by an off-line comparison between an astrometric measurement of the Earth rotation and an inertial measurement of the angular velocity of the laboratory. It is shown that the former, by means of routine observations of Very Long Baseline Interferometry, has already reached the accuracy needed to perform a 3 % experiment on a time span of ∼1 yr. We propose to perform the latter by a dynamical detector of local rotation of novel conception, the Gyromagnetic Electron Gyroscope. Its principle of operation is briefly discussed together with its response to rotationlike gravitational fields.

Toroidal SQUID with ferromagnetic core superconducting transformer

Ferromagnetic cores have been used for the secondary of a superconducting flux transformer in connection with a toroidal SQUID. Circuit analysis predicts an easier matching of the transformer for large inductances of the primary. Experimental data show a general agreement with the circuit analysis and a comparatively small increase in noise due to the metallic core.

Low temperature properties of soft magnetic materials: Magnetic viscosity and 1/f thermal noise

We study the magnetic properties of soft ferromagnetic cores in the low field linear regime at low temperature (T≤4.2 K) in view of their use in connection with superconducting quantum interference device magnetometers. We have tested several amorphous and polycrystalline alloys in the form of strip‐wound toroidal cores. Both high and near zero magnetostrictive alloys are studied. All samples are found out to be the source of thermal magnetic noise of 1/f spectral density in agreement with the fluctuation dissipation theorem. This type of thermal noise comes from a frequency independent imaginary permeability. This feature is equivalently described in terms of the magnetic viscosity effect or by considering the constant (residual) term in the classical Legg’s equation of magnetic losses at low fields. Measurements on a few Co‐based amorphous alloys show that the magnetic viscosity is independent of temperature. Explanations in terms of thermal activation processes and quantum tunneling are discussed.

Superconducting susceptometer for high‐accuracy routine operation

We present a new version of a SQUID susceptometer with the following performance. The overall accuracy is δχ≃3×10−9 (SI units). Within this figure is allowed the reproducibility in interchanging samples, the thermal expansion of the samples up to 10%, and the constancy of the calibration over a time scale of months. The sample can be interchanged in minutes and the overall time taken by the actual measurement procedure, to give results within the accuracy quoted above, is of the order of 5 min for one sample at one temperature. The temperature regulation is precise within 0.2 K between 40 and 300; the accuracy in the sample temperature has been tested to be within 0.5 K in the room temperature range. This performance is of great relevance for studies of biological molecules in solution, when different samples in different solution conditions must be compared with accuracies better than parts in a thousand of the magnetic susceptibility of the solution.

Loss budget of a setup for measuring mechanical dissipations of silicon wafers between 300 and 4 K

A setup for measuring mechanical losses of silicon wafers has been fully characterized from room temperature to 4 K in the frequency range between 300 Hz and 4 kHz: it consists of silicon wafers with nodal suspension and capacitive and optical vibration sensors. Major contributions to mechanical losses are investigated and compared with experimental data scanning the full temperature range; in particular, losses due to the thermoelastic effect and to the wafer clamp are modeled via finite element method analysis; surface losses and gas damping are also estimated. The reproducibility of the measurements of total losses is also discussed and the setup capabilities for measuring additive losses contributed by thin films deposited on the wafers or bonding layers. For instance, assuming that additive losses are due to an 80-nm-thick wafer bond layer with Young modulus about ten times smaller than that of silicon, we achieve a sensitivity to bond losses at the level of 5x10(-3) at 4 K and at about 2 kHz.

Magnetic viscosity, thermal relaxation, and thermal equilibrium noise in Co‐based amorphous alloys at milliKelvin temperatures

We report measurements of the magnetic reversible complex permeability and of the related thermal noise for a few Co‐based soft ferromagnetic amorphous alloys. The measurements were performed in the 16 mK–4.2 K temperature range and in the 0.1 Hz–1 kHz frequency range with a superconducting quantum interference device magnetometer. The data show the existence of a temperature independent magnetic viscosity together with a thermal relaxation of the spin subsystem to the heat bath. This last feature shows up as a partial rolloff of the real permeability from an isothermal low‐frequency value to an adiabatic high‐frequency one. The noise due to the sample is found in good agreement with the standard fluctuation‐dissipation prediction for the thermal noise.We report measurements of the magnetic reversible complex permeability and of the related thermal noise for a few Co‐based soft ferromagnetic amorphous alloys. The measurements were performed in the 16 mK–4.2 K temperature range and in the 0.1 Hz–1 kHz frequency range with a superconducting quantum interference device magnetometer. The data show the existence of a temperature independent magnetic viscosity together with a thermal relaxation of the spin subsystem to the heat bath. This last feature shows up as a partial rolloff of the real permeability from an isothermal low‐frequency value to an adiabatic high‐frequency one. The noise due to the sample is found in good agreement with the standard fluctuation‐dissipation prediction for the thermal noise.

Gravitational-wave stochastic background detection with resonant-mass detectors

In this paper we discuss how the standard optimal Wiener filter theory can be applied, within a linear approximation, to the detection of an isotropic stochastic gravitational-wave background with two or more detectors. We apply then the method to the AURIGA-NAUTILUS pair of ultralow temperature bar detectors, soon to operate in coincidence in Italy, obtaining an estimate for the sensitivity to the background spectral density of ’10 249 Hz 21 , that converts to an energy density per unit logarithmic frequency of ’8310 25 3r c , with r c’1.9310 226 kg/m 3 the closure density of the Universe. We also show that by adding the VIRGO interferometric detector under construction in Italy to the array, and by properly reorienting the detectors, one can reach a sensitivity of ’6310 25 3r c . We then calculate that the pair formed by VIRGO and one large mass spherical detector properly located in one of the nearby available sites in Italy can reach a sensitivity of ’2310 25 3r c while a pair of such spherical detectors at the same sites of AURIGA and NAUTILUS can