Superfluid Gyroscope Research Articles

Reflections on 65 Years of Helium Research

In this autobiographical article, I discuss a number of topics that have absorbed my interest over the years and illustrate how advances in experimental technique, such as the superfluid gyroscope and torsional oscillators, were entwined with expanding knowledge of the properties of helium.

Phase fluctuation noise adaptive cancellation system of superfluid gyroscope

Phase fluctuation noise adaptive cancellation system of superfluid gyroscope

Range extension design on superfluid gyroscope based on overlap factor optimization

Range extension design on superfluid gyroscope based on overlap factor optimization

Frequency-dependent hydrodynamic inductance and the determination of the thermal and quantum noise of a superfluid gyroscope

We reexamine mass flow in a superfluid gyroscope containing a superfluid Josephson weak link. We introduce a frequency-dependent hydrodynamic inductance to account for an oscillatory flow of the normal fluid component in the sensing loop. With this hydrodynamic inductance, we derive the thermal phase noise, and hence the thermal rotational noise of the gyroscope. We examine the thermodynamic stability of the system based on an analysis of the free energy. We derive a quantum phase noise, which is analogous to the zero-point motion of a simple harmonic oscillator. The configuration of the studied gyroscope is analogous to a conventional superconducting RF SQUID. We show that the gyroscope has very low intrinsic noise $(1.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}\mathrm{rad}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}∕\sqrt{\mathrm{Hz}})$, and it can potentially be applied to study general relativity, Earth science, and to improve global positioning systems (GPS).

Superfluid gyroscope with cold atomic gases.

A trapped Bose-Einstein condensed atomic gas containing a quantized vortex is predicted to exhibit precession after a sudden rotation of the confining potential. The equations describing the motion of the condensate are derived and the effects of superfluidity explicitly pointed out. The dependence of the precession frequency on the relevant parameters of the problem is discussed. The proposed gyroscope is well suited to explore rotational effects at the level of single quanta of circulation.

The role of the Josephson-Anderson equation in superfluid helium

This article explains how a simple equation describing the time evolution of a superfluid's quantum phase can be used as a powerful tool to rapidly deduce exact magnitudes of physical observables in situations involving very complex vortex motion. The equation has been used to simplify the understanding of new phenomena, such as vortex precession. Applications of the equation have also led to solutions of long-standing problems, such as the nucleation of vortices, and to new technology, such as the superfluid gyroscope. The article begins by presenting some basic ideas of superfluidity. This discussion leads to the concept of the quantum phase of the superfluid state and to the prediction that vorticity is quantized. Next a discussion is presented of the phase evolution equation, introduced by Josephson and developed further by Anderson. The utility of the equation is demonstrated by making certain general predictions about the consequences of vortex motion. Two experiments, one in ${}^{3}\mathrm{He}$ and another in ${}^{4}\mathrm{He},$ are then described in the context of the phase evolution equation. In the first, the precession frequency of a single vortex filament is easily explained in the context of the equation. In the second, quantized dissipation processes are observed which give detailed information about the creation of quantized vortices. The article concludes by showing how these latter experiments have led to the development of a superfluid sensor of absolute rotation. Although the article focuses on results emerging from the author's own laboratory, the footnotes lead the reader to some of the parallel ongoing projects, especially in the case of the ${}^{4}\mathrm{He}$ research at Orsay/Saclay in France, the University of Minnesota, and the University of Trento, Italy.

Detection of absolute rotation using superfluid He4

We have developed the superfluid analog of the superconducting rf SQUID. Such a device is a quantum mechanically based, absolute gyroscope and has been used to sense the rotation of the Earth. Our device is fabricated using silicon processing techniques and forms a planer sensing loop of superfluid helium which couples to the applied rotation. A much more sensitive superfluid gyroscope based on the principle’s demonstrated with this device, might ultimately be used to detect the precession of our local inertial frame with respect to the fixed stars by the gravitomagnetic field of the rotating Earth. We compare the superfluid gyroscope against two other experiments aimed at detecting this general relativistic effect.

Monitoring Earth orientation through the end of the century

In 1992 Very Long Baseline Interferometry (VLBI) is the “method of choice” to monitor polar motion (PM), Universal Time (UT1), precession and nutation. International VLBI networks routinely produce PM and nutation values accurate to 0.3–0.5 milli-arc-seconds (mas) and UT1 accurate to 0.05 milliseconds (ms), at 3.5 day intervals, and daily UT1 values accurate to 0.05–0.10 ms. Only cost considerations prevent sub-daily PM and UT determinations. Future improvements in VLBI should achieve 0.05–0.10 mas accuracies, and near real time correlation could reduce processing delays to 24 hours; the Global Positioning System (GPS) may provide PM at 2–6 hour intervals, while single baseline VLBI observations could provide UT1 values at comparable intervals. Eventually the combination of real-time processing of GPS plus superfluid gyroscope data may provide nearly continuous PM and UT1 tracks for periods of weeks; infrequent VLBI sessions will be needed for monitoring precession, nutation, and the celestial and terrestrial reference frames.

New Superfluid Relativity Gyroscope

Experiments have been performed in which mechanical radiation pressure, generated by a megahertz sound field in helium II, successfully supported a metal sphere three dimensionally. Because the field's forces are spherically symmetrical and stable, and because the isothermal environment provided by the quantum coherence properties of helium II eliminates convection currents, only extremely small stray torques act on the suspended mass. It is demonstrated that stray torques less than 10−7 dyn cm were present on the early test model, consistent with the theoretical predictions. Also presented is the predicted performance, based upon these results, of a more refined superfluid gyroscope which demonstrates the feasibility of observing general relativistic gyroscopic motion with a gyroscope rigidly connected to the earth. A proposed experiment to discriminate between Einstein's theory and competing theories of gravitation by measuring the spin-spin interaction between a gyroscope and the spinning earth is also discussed.

Application of a Superfluid Gyroscope to the Study of Critical Velocities in Liquid Helium Near theλTransition

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