A preliminary study of a cryogenic equivalence principle experiment on Shuttle

The Weak Equivalence Principle is the hypothesis that all test bodies fall with the same acceleration in the same gravitational field. The current limit on violations of the Weak Equivalence Principle, measured by the ratio of the difference in acceleration of two test masses to their average acceleration, is about 3 parts in one-hundred billion. It is anticipated that this can be improved in a shuttle experiment to a part in one quadrillion. Topics covered include: (1) studies of the shuttle environment, including interference with the experiment, interfacing to the experiment, and possible alternatives; (2) numerical simulations of the proposed experiment, including analytic solutions for special cases of the mass motion and preliminary estimates of sensitivity and time required; (3) error analysis of several noise sources such as thermal distortion, gas and radiation pressure effects, and mechanical distortion; and (4) development and performance tests of a laboratory version of the instrument

Superconducting bearings for application in cryogenic experiments in space

Linear superconducting magnetic bearings suitable for use in a proposed orbital equivalence principle experiment and for general application in space were developed and tested. Current flows in opposite directions in adjacent superconducting wires arranged parallel to the axis of a cylinder. This configuration provides maximum stiffness radially while allowing the test mass to move freely along the cylinder axis. In a space application, the wires are extended to cover the entire perimeter of the cylinder: for the earth-based tests it was desirable to use only the bottom half. Control of the axial position of the test mass is by small control coils which may be positioned inside or outside the main bearing. The design is suitable for application to other geometries where maximum stiffness is desired. A working model scaled to operate in a 1-g environment was perfected approximate solutions for the bearings were developed. A superconducting transformer method of charging the magnets for the bearing, and a position detector based on a SQUID magnetometer and associated superconducting circuit were also investigated

Nonlinear backreaction in a quantum mechanical SQUID

In this paper we discuss the coupling between a quantum mechanical superconducting quantum interference device (SQUID) and an applied static magnetic field. We demonstrate that the backreaction of a SQUID on the applied field can interfere with the ability to bias the SQUID at values of the static (DC) magnetic flux at, or near to, transitions in the quantum mechanical SQUID.Comment: 9 pages, to be published in Phys. Rev.

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.Comment: 7 pages, 3 figure

Control of Multi-level Voltage States in a Hysteretic SQUID Ring-Resonator System

In this paper we study numerical solutions to the quasi-classical equations of motion for a SQUID ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g. 10 state), multi-level logic and memory.Comment: 8 pages, 9 figure

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

Signatures of chaotic and non-chaotic-like behaviour in a non-linear quantum oscillator through photon detection

The driven non-linear duffing osillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravellings of the master equation. In order to generated such trajectories in the phase space of this oscillator in this paper we use a the quantum jumps unravelling together with a suitable application of the correspondence principle. We analyse the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localisation of the wave packet from the measurement of the oscillator by the photon detector produces a concomitant structure in the power spectra of the measured output. Furthermore, we demonstrate that this spectral analysis can be used to distinguish between different modes of the underlying dynamics of the oscillator.Comment: 7 pages, 6 figure