SQUID-based Technique to Study the Elastic Properties of Solids at Very Low Temperatures

Mechanical oscillators are widely used for measurements of the elastic properties of solids at low temperatures. In most of such experiments mechanical displacements are detected via capacitive changes. In order to improve the sensitivity we have developed a novel detection technique relying on the high sensitivity of a commercial dc SQUID. To demonstrate the performance of the new setup we have measured the variation of the sound velocity and the internal friction of vitreous silica and of the borosilicate glass BK7 in the temperature range from 5 mK to 1 K. Our results agree favorably with former experiments where the displacement was detected capacitively. Furthermore, our results confirm that deviations of the elastic behavior of amorphous solids from the predictions of the standard tunneling model exist at very low temperatures.      

Acoustic Properties of an Amorphous Silica Oscillator at mK Temperatures

We have studied the acoustic behavior of an a-SiO₂ composite torsional oscillator in the temperature range between 1 and 100 mK. At higher temperatures, the acoustic properties of amorphous solids are well described by the ‘tunneling model’. However, below 10 mK it was found that the resonance exhibited a non-Lorentzian shape and was highly distorted by random ‘noise’. We attribute this stochastic noise—‘transients’ to interactions of a-SiO₂ with ambient γ quanta present in the laboratory. By shielding the cryostat with a 5 cm thick lead wall we were able to reduce the number of transients. On the other hand, a deliberately introduced 6.1μCi ²²Na source of γ radiation caused the opposite effect. We interpret the transients in the framework of local heating caused by the interaction between photons and amorphous SiO₂ which changes the elastic properties of the oscillator. Our findings have potential applications for particle detection.     

NQR on Gallium Single Crystals for Absolute Thermometry at Very Low Temperatures

It is shown that NMR/NQR-thermometry on Ga single crystals can serve the need of absolute thermometry in a temperature range from below 20 K to above 1 mK. Thus, the sensitive range includes all phase transition temperatures around 1 mK of solid and fluid ³ He, a necessity for an extension of the ³ He-melting-pressure temperature scale towards lower temperatures. The experiments were performed in magnetic fields of 50 to 200 mT and at temperatures down to 200 K using single rf-pulses. Special care was taken for the orientation of the magnetic field with respect to crystal orientation which was obtained by in-situ pulsed NMR-experiments. It has been shown that in the investigated parameter range nonlinear effects in NMR due to high spin alignment had no significant influence. In pulsed NMR as well as in specific heat experiments it could be shown that spin-spin interactions are only weak in Ga and do not influence nuclear paramagnetism, at least at temperatures above 100 K. The advantages of using Ga instead other elements for population difference thermometry are discussed.     

Vortex Dynamics in Superfluid 4He at Very Low Temperatures

Recently McClintock et al. observed the free decay of a vortex tangle in superfluid ⁴He at mK temperatures. Since the system at such low temperatures is free from normal fluid and usual mutual friction, the mechanism of the free decay is unknown. In order to understand this phenomenon, this work studies numerically the vortex dynamics without the mutual friction. The absence of mutual friction prevents the vortex from smoothing. The resulting kinked structure promotes vortex reconnection, thus making lots of small vortex loops. Such cascade process as breakup of vortices to smaller ones can decay the vortex line density. This paper describes the decay of vortex tangle under the localized induction approximation, and that of four vortex rings under the full nonlocal calculation.     

Non-equilibrium Dynamics of Interacting Tunneling States in Glasses

After the temporary application of a strong electric bias field to a glass sample at temperatures in the milli-Kelvin range its dielectric constant is increased and then decays slowly back to its equilibrium value. We studied these dielectric non-equilibrium properties of the polyester glass Mylar and the borosilicate glass BK7 as a function of bias field and temperature. We find that the decay to equilibrium depends on the duration of the applied bias field substantially only if the sample has been biased for several thousand seconds or longer. The decay curves after shorter bias field applications are influenced rather by the rate by which the field has been changed. Following the ”dipole gap” theory¹ we assume that the observed excess dielectric response originates in the non-equilibrium dynamics of tunneling states (TSs) that are strongly coupled. Our analysis of the data within the framework of strongly coupled pairs of TSs indicates three competing equilibrium destroying processes, leading to the observed dynamics. Obviously the energy relaxation rate of TSs depends on the bias field since it changes the energy splitting of TSs by coupling to their dipole moments. In addition, a quick enough field sweep can drive TSs non-adiabatically between their energy eigen-states yielding sweep rate dependent decay times. The third process results in decay times independent of temperature and the bias field sweep rate and duration. We propose a picture where the field lifts the tunneling particle in potential wells beyond its original double well as the cause of the third contribution. The decay towards equilibrium is by quantum mechanical tunneling. Moreover, our observations indicate that below a material dependent temperature the relaxation of TSs is caused primarily by interactions between them. PACS numbers: 61.43.Fs, 05.70.Ln, 66.35.+a, 77.22.-d     

A New Device for Studying Low or Zero Frequency Mechanical Motion at Very Low Temperatures

We have developed a new ??floppy wire?? device for studying the motion through quantum fluids and solids at very low temperatures. The device is particularly well suited for producing large amplitudes of motion, for measuring drag forces at low frequency, and for studying ??zero?? frequency dynamics by measuring transient behavior. The device is very versatile and allows motion to be studied over a broad range of velocities and amplitudes. It generates negligible heat leaks and so is ideally suited for ultra low temperature experiments. The device has many potential applications in quantum fluids and solids research, including the study of drag forces at low frequencies in both the laminar and turbulent flow regimes, and the investigation of motion in (super)solid ⁴He. We discuss the principles and modes of operation of the device and present some preliminary measurements in vacuum, in normal liquid ³He and in superfluid ⁴He. We also present measurements of a ??floppy grid?? device, which could be used for generating large volumes of quantum turbulence in superfluids at low temperatures.     

The Nucleation of Superfluid Turbulence at Very Low Temperatures by Flow Through a Grid

Recent experiments by Nichol et al. (cond-mat/0309245 v2) have been concerned with the dynamical behaviour of a grid oscillating in superfluid ⁴He at a very low temperature, where the normal fluid can be ignored. An interesting enhancement of the effective mass of the grid was observed above a first threshold velocity, without significant increase in damping. Only above a second larger threshold was there a large increase in damping, resulting, we presume, from the generation of turbulence. We show now how the increase in effective mass can be understood in terms of an adiabatic response of the remanent quantized vortices that are knoum to be present, usually, in superfluid helium. Only at the larger threshold is the adiabatic response replaced by a dissipative evolution into a turbulent tangle of vortex lines. We present a semi-quantitative analysis of the experimental results, which suggests strongly that the remanent vortices must take the form of a rather high density of vortex loops attached to the grid. But confirmation of our ideas must await the completion of further experiments and a programme of non-trivial computer simulations.     

Kelvin-Wave Cascades in Turbulent Superfluid 4He at Very Low Temperatures

There has been much interest recently in the mechanism by which superfluid (quantum) turbulence can decay in liquid ⁴He at very low temperatures, where mutual friction has a negligible effect. As in classical turbulence, energy must probably flow from larger to smaller length scales, and it has been suggested that on the smallest scales the relevant motion is a Kelvin wave on a quantized vortex with wave number greater than the inverse vortex spacing. By considering the behaviour of a simple model it is shown by computer simulations how energy can flow to shorter length scales (higher wave numbers) in a system of Kelvin waves, and how this process can lead to a remarkably simple Kelvin-wave energy spectrum. A discussion is included of the relevance of this model to the decay of superfluid grid turbulence at a very low temperature.     

Logarithmic Temperature Dependence of the Sound Speed in Amorphous Silica at Low Temperatures

The tunneling model has enjoyed considerable success in describing the low temperature properties of glasses. However, departures from the tunneling model have been noted in experiments at very low temperatures (below 100 mK). We have measured the change in the sound speed ΔV/V ₀ between 1 and 40 mK in an amorphous silica double paddle oscillator oscillating at 14 kHz. Most importantly, the sound speed displayed the logarithmic temperature dependence predicted by the tunneling model to a lower temperature than in previous experiments on amorphous silica. Below 3 mK the sound speed departed from the logarithmic temperature dependence and began to level off. The leveling off can be explained by either an intrinsic effect or thermal decoupling of the sample from the thermometer. By heating the oscillator with a gamma source to determine the thermal resistance of the oscillator, it was found that a relatively large stray heat input (9×10⁻⁴ nW) would be needed to cause the leveling off. Further work will be needed to determine whether the leveling off is due to stray heat or intrinsic physics.     

The Dynamic Texture of Superfluid 3He-B at Very Low Temperatures and in High Magnetic Fields

No Heading We report experiments using a pair of crossed vibrating wire resonators (VWRs) in the B phase of superfluid ³He in the zero temperature ballistic limit and in magnetic fields up to the B to A phase transition field of 340 mT. The VWRs are sensitive mechanical probes of energy gaps, textures and turbulent flow. In high magnetic fields the energy gap is no longer isotropic but significantly distorted, and the damping measured by the VWRs increases. With the crossed pair, we find that we can reduce the damping measured by one VWR when we increase the drive on the other one. We suggest that the reduction arises from the orientation of the surrounding texture by superflow and the screening of quasiparticles by the creation of superfluid turbulence.PACS numbers: 67.57.Fg, 67.57.Hi.     

欠时效态3J21合金低温拉伸性能

在万能拉伸机上对欠时效态3J21合金室温及低温条件下的拉伸性能进行研究,并采用金相显微镜、X射线衍射仪对冷轧状态和欠时效态的金相组织及物相进行分析,采用TEM观察两种状态的组织和结构,验证了X射线衍射结果.对欠时效态3J21合金不同温度下拉伸断口附近形变显微组织进行分析,采用扫描电镜(SEM)对拉伸断口进行观察.结果表明:欠时效态3J21合金的室温断口为韧窝断口,而低温断口呈现混合断裂特征.随着温度降低,脆性断裂的特征更为明显,低温拉伸断口附近显微组织中可发现孪晶数量随温度的降低而增加;欠时效态3J21合金的抗拉强度和屈服强度随温度的降低而明显提高,其中抗拉强度提高的幅度较大,而延伸率略有下降.对室温和低温对欠时效态3J21合金拉伸性能的影响进行了讨论.     

Measurements on a Dynamic A-B Phase Boundary in Superfluid 3He at Very Low Temperatures

We present preliminary measurements of the dynamics of a moving A-B phase interface in superfluid ³ He at temperatures below 0.2T _c We initially stabilise the interface at low temperatures with a shaped magnetic field. We can then move the interface in a controlled manner by applying small additional time-dependent fields. The interface is created inside a quasiparticle radiator consisting of a cylindrical chamber in weak thermal contact with the refrigerant. Vibrating wire resonators inside the radiator allow us to monitor the temperature of the superfluid and to infer the heat generated by the interface motion. When we oscillate the interface at low frequencies, we measure spectacular oscillatory swings of the liquid temperature arising from the enormous change in the low lying density of states as the volume of the A-phase superfluid is alternately compressed and expanded. We have also observed hysteresis in the transition as a function of magnetic field. In particular, we observe a small history-dependent super-magnetisation of the B-phase prior to A-phase nucleation in the experimental chamber. When the system is in the metastable super-magnetised state we are able to observe a higher nucleation probability of the A-phase when the cryostat is exposed to neutrons.     

Relationship Between Interatomic Separation and Pressure for Ionic Solids at High Temperatures

The equation of state derived from the Anderson approximation and the theory of interionic potentials based on the quantum mechanical form of the overlap repulsive energy are used to investigate the relationship between interatomic separation and pressure for three ionic solids (LiF, NaF, and CsC1) at high temperatures. The values of van der Waals dipole–dipole and dipole–quadrupole energies are also included in the model. The results obtained are in agreement with the available experimental data.     

Thermodynamic Properties of a Double Ring-Shaped Quantum Dot at Low and High Temperatures

In this work, we study thermodynamic properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. To this end, we first solve the Schrödinger equation and obtain the energy levels and wave functions, analytically. Then, we calculate the entropy, heat capacity, average energy and magnetic susceptibility of the quantum dot in the presence of a magnetic field using the canonical ensemble approach. According to the results, it is found that the entropy is an increasing function of temperature. At low temperatures, the entropy increases monotonically with raising the temperature for all values of the magnetic fields and it is independent of the magnetic field. But, the entropy depends on the magnetic field at high temperatures. The entropy also decreases with increasing the magnetic field. The heat capacity and magnetic susceptibility show a peak structure. The heat capacity reduces with increasing the magnetic field at low temperatures. The magnetic susceptibility shows a transition between diamagnetic and paramagnetic below for \(T<4\hbox { K}\). The transition temperature depends on the magnetic field.     

Epitaxial Si Sensors at Low Temperatures: Non-Linear Effects

Cryogenic bolometric sensors made from epitaxially grown Si:As have been tested down to 40 mK. The sensors were grown by chemical vapour deposition with a doped layer 8.4 μm thick. The dopant concentration was measured using SIMS and was constant, ±1%, with an excellent box profile. Arsenic concentrations up to 7.5×10¹⁸ cm⁻³ were achieved. Above 100 mK the low power resistanceR(T) followed the variable range hopping law, or Efros-Shklovskii law for a Coulomb gap,R(T)=R ₀ exp(T ₀/T)^1/2 withT ₀∼25 K, typically. A double sensor arrangement was used to measure the electronphonon coupling in the sensors and the phonon coupling to the heat sink. As the dc current bias through a sensor was increased, spontaneous voltage oscillations were observed across the sensor below 100 mK, which limited the sensitivity of the sensors in this region. These are circuit-limited oscillations between high and low resistance states. A phase diagram was established for the spatio-temporal coexistence of the two states, with a critical temperatureT _c=115 mK. We show that this is an intrinsic phase transition within a thermal model of the electron-phonon coupling. For a resistance-temperature characteristic given by the Efros-Shklovskii law we findT _c=0.00512T ₀, independent ofR ₀ and the coupling strength. This predictsT _c=115±4 mK in this case. The model gives excellent agreement for the critical voltage and current, by assuming that the breakdown occurred via the formation of a filamentary region of high current density and high electron temperature. At higher currents, the response was temperature independent and given byI(E)=I(0) exp{−(E ₀/E)^1/2} whereE is the average applied electric field andE ₀∼380 V/cm, in agreement with a thermal model which includes the phonon-phonon coupling to the heat sink.     

Low Temperature Acoustic Properties of Poly-Crystalline Aluminium

As in other structurally disordered solids, the low temperature acoustic properties of poly-crystalline aluminium are governed by atomic two-level tunneling systems. The particular temperature variation of sound velocity and internal friction depends on the dynamical behaviour of these tunneling systems, which is expected to be determined by interaction with thermal phonons and conduction electrons as in metallic glasses. In earlier measurements on aluminium-wires no significant difference was found whether the sample was superconducting or kept in the normal state by a sufficiently high magnetic field and the concluding claim was ‘absence of electron-assisted relaxation for tunneling systems in poly-crystalline metals’. In this report, vibrating reed measurements are presented of pure poly-crystalline Al with a special sample shape that reduces the influence of the clamping. We in fact find significant differences between the sample being normal conducting or superconducting. The overall behaviour indeed resembles very closely that of metallic glasses and clearly demonstrates that also in Al tunneling systems couple to conduction electrons as expected. As a quantitative result we may state that the density of states of tunneling systems in poly-crystalline Al is considerably smaller than in metallic glasses. PACS numbers: 61.43.-j, 62.65.+k, 63.50.+x