Torsional Oscillator Experiments under DC Rotation with Reduced Vibration

We describe a highly stable, rotating cryostat designed for torsional oscillator experiments under DC rotation, where vortex lines penetration has been studied for 3D superfluids made of monolayer He films as well as for the supersolid state in hcp solid ⁴He. Especially, torsional oscillator experiments on hcp solid ⁴He are known to be quite sensitive to small vibrations or linear velocities on the order of 10 ??m/s or less. Thus, vibrations of the apparatus may destroy the measurements if they are not smaller than or equal to those of the building or the ground itself. The torsional oscillator performance described here often gives better data under steady rotation at moderate speeds than under stationary conditions. The article describes briefly a design idea shared by the two rotating cryostats at ISSP, the University of Tokyo, and discusses the torsional oscillator (TO) experiments under DC rotation. This is truly a high speed rotating cryostat with maximum rotational speed of at least 6 revolutions per second for TO experiments. It gives also much higher stability at reasonably low rotational speed because of the well-planned structure of the double frame construction with a lot of mass for the upper drive frame for rotation and the almost mechanically isolated, except for the drive mode motion, rotating cryostat with much higher stability of the inner frame for the cryostat mount. Phenomena of quantized vortex lines penetration through a macroscopic superfluid give unique information about the superfluidity itself. A method for detection of vortex lines penetration events using TO technology is also briefly reviewed.     

Torsional Oscillator Study of Thin He Films Under High Speed Rotation

Superfluidity is often compared with superconductivity and rotation is contrasted with magnetic field. In the case of superconductors, it is possible to destroy the superconducting state by application of a sufficiently high magnetic field. Agthough it is not yet technically feasible to destroy the superfluid state through rotation, significant modification of the superfluid can be achieved through rotation. In the experiments reported here we are studying the influence of rotation on the dissipation in superfluid films adsorbed in a porous medium. A new peak in the film dissipation is observed while under rotation at a temperature somewhat below the transition temperature. The dissipative feature we observe is related to the resugt for 2D films under rotation previously reported by Adams and Glaberson, however our observations for films in a porous medium under rotation differ considerably in detail. A theoretical discussion of these resugts has recently been given by Fukuda, et al. (to be published).     

Switching of Dislocations in Solid Helium Between Pinned and Unpinned States in the Torsional Oscillator Experiments

The anomalous temperature dependence of the period of a torsional oscillator (TO) containing solid helium can be explained by the dislocation-vibration model. Namely, the dislocations in solid helium vibrate in phase with the torsional oscillation and the TO-period change varies as the square of the average dislocation pinning length which becomes shorter at lower temperature due to pinning of dislocations by ³He impurity atoms. This dislocation-vibration model is further developed by introducing distribution functions for the network pinning lengths for dislocation segments and by considering the mechanisms of pinning of dislocations by and unpinning of dislocations from ³He impurity atoms. Experimental data, such as the TO-period change at different ³He concentrations, the rim-velocity dependence of the TO period, the hysteresis of the TO period with respect to the rim velocity and to the temperature, are analyzed based on the dislocation-vibration model. Above all, the hysteresis is caused by switching of dislocations between pinned and unpinned states.     

Effect of Helium Elasticity on Torsional Oscillator Measurements

In 2004 Kim and Chan performed a torsional oscillator measurement of the rotational inertia of solid helium-4. They found frequency changes which were interpreted in terms of a non-classical rotational inertia, that is a partial superfluidity or ??supersolidity?? of solid helium-4. Since then there have been many further studies using various versions of this technique. One important question that arises in these experiments is the possible effect on the oscillator frequency of changes in the elasticity of the solid helium; this can produce a change in frequency that adds to any effect due to superfluidity. In this paper we give a general discussion of the effect of changes in elasticity on the oscillator frequency and consider how the magnitude of the effect is influenced by the oscillator design. Our results should help make it possible to discriminate between frequency changes due to changes in elasticity and changes due to supersolidity.     

Interpreting Torsional Oscillator Measurements: Effect of Shear Modulus and Supersolidity

The torsional oscillator is the chief instrument for investigating supersolidity in solid ⁴He. These oscillators can be sensitive to the elastic properties of the solid helium, which show anomalies over the same range of temperature in which the supersolid phenomenon appears. In this report we present a detailed study of the influence of the elastic properties of the solid on the periods of torsional oscillators for the various designs that have been commonly employed in supersolid measurements. We show how to design an oscillator which measures supersolidity, and how to design one which predominantly measures elasticity. We describe the use of multiple frequency TOs for the separation of the elastic and supersolid phenomena.     

Torsional Oscillator Study of Thin Helium Films on Hydrogen Substrates

We have made torsional oscillator measurements of thin helium films on a Mylar surface preplated with 2 and 5 layers of H ₂ . The minimum ⁴ He coverage needed for superfluidity, or inert layer, n _o on both surfaces is found to be 6 mole/m ² . This is equivalent to 1/2 of a monolayer at bulk liquid density. The superfluid transition in coverages above n _o is similar to that found on bare Mylar, exhibiting the standard Kosterlitz-Thouless characteristics. We find no anomaly in _s or the dissipation in the film that can be identified with a second transition reported in recent third sound experiments.     

Frequency-Domain Interpretation of Oscillator Phase Stability

A frequency-domain interpretation of the phase stability of an oscillator is discussed. From a knowledge of the time dependence of an oscillator phase during a time interval T* it is possible to give the characteristics of this oscillator, not only for this time interval, but also for subsequent time intervals. Since the use of a Fourier transform for the computation of a continuous power spectrum is unrealistic, a discrete-spectrum approach will be taken. Usually, in the calculation of power spectra, stationarity of the fluctuations is assumed, although experiment indicates that this is often not the case. A more realistic approach is adopted. Analytical phenomena and random walk are separated from white noise on the basis of statistical criteria using discrete Fourier transforms. The white noise is then interpreted in the frequency domain. Both random walk and specific signals are studied in the time domain and can be separated by digital filtering. Two different sets of experimental results are analyzed by this method, one derived from measurements on a quartz-crystal oscillator locked to a low-frequency transmitter and the second from measurements on an ammonia maser. In both cases, measurement precision and ease of prediction of the behavior of the oscillator are improved.     

Comparison between Torsional Oscillator and Ultrasonic Measurements of 4He Confined in Nano-Porous Media

We have performed torsional oscillator and ultrasonic measurements for ⁴He confined in 2D nano-porous substrate, hectorite. For ⁴He films, the resonance frequency of the torsional oscillator increases rapidly just below a superfluid transition temperature (T _C ), and then becomes constant at the lower temperature. In contrast, the sound velocity below T _C increases monotonically with decreasing temperature. For liquid ⁴He the sound velocity has a small bend at T _b of about 0.9 K. Its increase below T _b is enhanced as the pressure is increased.     

Frequency Stability Analysis of Transistorized Crystal Oscillator

This paper gives an analysis of a modified Pierce oscillator for frequency variation due to changes in the circuit or transistor. The magnitudes of the frequency shifts due to parameter changes are computed in relation to each other. The analysis has been verified by testing the oscillator circuit with several transistors which had significantly different measured parameters. Computed frequency shifts were compared with measured frequency shifts. The agreement between experimental and calculated data is ?8×10-9 with a 5 Mc, fifth overtone quartz crystal in the circuit. A general equation relating frequency changes to changes in circuit parameters has been derived and is applicable to any operating frequency as long as the y parameters of the transistor and the circuit elements of the oscillator are known.     

高稳晶振的秒级频率稳定度的测量

介绍了在不同的条件下，对高稳晶振的秒级频率稳定度进行测量的方法。     

Torsional Oscillator Measurements of Liquid 4He Confined in 2.2-nm Channels of FSM

We have performed torsional oscillator measurements for liquid ⁴He confined in 2.2-nm channels of FSM up to 2.45 MPa. At 0.1 MPa, the resonant frequency increases with decreasing temperature. It shows a small bend at about 0.9 K, and then keeps increasing down to the lowest temperature, 0.16 K. The magnitude of the frequency increase below 0.9 K is suppressed with increasing pressure, while the temperature of the bend shows almost no pressure dependence.      

Simultaneous Measurements of an Ultrasound and a Torsional Oscillator for 4He in a Nanoporous Glass

Previously, we carried out ultrasonic measurements for liquid ⁴He filled in a nanoporous glass (Gelsil), and observed an increase in the sound velocity due to decoupling of the superfluid component. At zero pressure, the superfluid transition temperature T _C is suppressed to 1.4 K from the bulk lambda point, 2.17 K. This behavior is the same as torsional oscillator measurements by Yamamoto et al. (Phys. Rev. Lett. 93:075302, 2004). However, the pressure dependence of T _C and the temperature dependence of the superfluid fraction are very different from the torsional oscillator measurements. In order to clarify the origin of the difference, we have developed a new technique of simultaneous measurement of an ultrasound and a torsional oscillator, and the system successfully works for a nanoporous glass. Here, we compare decoupling of the superfluid component for ⁴He films between an ultrasound and a torsional oscillator.     

具有分数阶形状记忆合金系统的时滞反馈控制与稳定性分析

将分数阶引入到形状记忆合金振子模型中,针对分数阶对其系统动力学的影响进行了研究。首先基于分数阶微分方程理论,构建了分数阶形状记忆合金系统,并给出了该系统的稳定性和Hopf分岔存在性条件。其次,设计了时滞反馈控制器,用来控制分数阶形状记忆合金系统的稳定性。研究结果表明,形状记忆合金系统中的时滞和分数阶对系统的动力学性质有着重要的调控作用。     

Low T Study of PdH x System by Torsional Oscillator Technique: x Dependent Responses

Hydrogen atoms dissolve in Pd at densities up to one H atom per Pd, which provides higher atomic H density than in solid H₂. They are known to have large diffusion coefficient due to quantum tunneling. Torsional oscillator?(TO) technique is employed to investigate the phases of H in Pd, which is known to show phase boundaries at the lowest T among metal-hydrogen (MH) systems. Specific heat measurements have been performed for PdH _x with x up to high H concentration specimens as well as studies of the resistivity study to establish the unique x?T phase diagram. We have, in addition, been performing TO experiments, in order to study the effect of atomic H intrusion and the dynamics in the PdH(D) _x system. The TO is a well-established, powerful instrument method to investigate superfluidity and quantum vortices of liquid He, especially in thin films, as well as dislocation dynamics in solids. In our TO experiments on PdH _x specimens have shown a resonance frequency shift for PdH _x , with 0.16??x??0.75 at the lowest T??s, which can be largely explained by the lattice deformation by H intrusion. This x dependent contribution has a smaller, additional change depending on x and T above ??50?K. We will show the details of experimental data and discuss the correspondence to the phonon modes change and further possibility of studying occurrence of quantum phenomena for the hydrogen system.     

晶体振荡器1s频率稳定度的测量及不确定度分析

本文介绍了电子测量仪器内石英晶体振荡的1s频率稳定度的测量方法并分析了测量值的不确定度。     

Periodical Oscillation Phenomena Observed in Salt-Water Oscillator Experiments under Small Gravity Conditions

We examined periodical oscillation phenomena that were observed during salt-water oscillator experiments under a small gravity condition. This condition was realized by situating a lower-density gadolinium chloride (GdCl ₃) aqueous solution on a higher-density sodium chloride (NaCl) aqueous solution and applying a downward magnetic force. The GdCl ₃ solution concentration was 0.15 mol/kg (density ρ=1.03×10³ kg/m ³), and the NaCl concentration was varied to (A) 4.35 mol/kg (ρ=1.15×10³ kg/m ³), (B) 3.79 mol/kg (ρ=1.12×10³ kg/m ³), and (C) 2.49 mol/kg (ρ= 1.09×10 ³ kg/m ³). The magnitude of magnetic flux density was varied from 0 to 4.00 T. As the magnetic flux density grew larger, the GdCl ₃ solution was pulled downward by the magnetic force, and upward and downward flows were generated simultaneously at the orifice. These flows were accompanied by a periodical, locally thickened part. The thickened part was only observed when the magnetic force magnitude was small in cases (A) and (B). This flow pattern was not observed in case (C), in which a conventional salt-water oscillation was induced instead (C). In this paper we discuss new experimental results in which the oscillation cycles in cases (A) and (B) are strongly associated with the magnitude of the magnetic force and the density difference in the biphase solutions.     

Double Torsional Oscillator Measurements for 4He Confined in 1D Nano-porous Medium FSM16 with a 2.8-nm Channel

We have studied the frequency dependence of superfluid response for ⁴He confined in a one-dimension nano-porous medium, FSM16, with 2.8-nm channel. The measurements were performed for an identical sample at two frequencies of 2000 and 500 Hz, by means of a double torsional oscillator. It was made clear that the rapid growth of superfluid response for the low frequency mode occurs at several tens mK lower than those for the high frequency mode. The difference between the two frequency modes is enhanced by the application of pressure. The observed frequency dependence suggests a dynamical superfluid peculiar to one dimension.     

边界激励非线性弹簧质量串响应的时空结构

本文研究边界激励下的非线性弹簧质量系统响应的时空特征，通过Ｐｏｉｎｃａｒｅ映射时间离散以及时间、空间谱及模式动力熵等的计算，发现了这一非线性系统的时空浑沌，并得出了一种时空结构随参量变化的新的演化机制．