C. D. H. Williams

Nonappearance of vortices in fast mechanical expansions of liquid He=4 through the lambda transition

A new experiment has been performed to study the formation of topological defects (quantized vortices) during rapid quenches of liquid He-4 through the superfluid transition, with particular care taken to minimize vortex creation via conventional hydrodynamic flow processes. It is found that the generated vortices, if any, are being produced at densities at least 2 orders of magnitude less than might be expected on the basis of the Kibble-Zurek mechanism.

Interactions between phonon sheets in superfluid helium

We have measured the effect of colliding two phonon sheets together at different angles. At small angles they interact strongly and a hot line is formed along the line of intersection of the two sheets. At angles between ~13? and ~27? the interaction becomes weaker and less energy goes into the hot line. At angles greater than ~27? there is no interaction between the sheets and they pass through each other. By delaying one sheet with respect to the other, the path of the hot line can be shifted laterally. Using this behaviour, we show that the sensitive area of the bolometer is around 10?2?mm2. We have measured the profile of the hot line and find that its width, typically 1?mm, varies as 1/sin(?/2), where ? is the angle between the two sheets. We analyse the data and estimate that the typical angle between two phonons interacting by the three phonon process varies between 8.4? and 12.5?, depending on their energy. We model the formation of the hot line when the sheets are strongly interacting. From the model and the measured data, we find that the temperature of the hot line decreases, and the cone angle and energy density of the hot line increases, with both increasing energy density in the sheets and increasing angle ?.

Creation of Quantized Vortices at the Lambda Transition in Liquid Helium-4

A fast (∼ 3 ms) adiabatic expansion of a volume of liquid4He through the lambda transition is being used to study the nature of the transition and to model the cosmological false vacuum to true vacuum phase transition of the early universe. Preliminary results are reported showing that, in accordance with theoretical predictions by W H Zurek (Nature 317, 505; 1985), there is copious production of quantized vortex lines, which represent the superfluid analogue of cosmic strings. The line density after the expansion appears to decay in two distinct stages, with a fast decay being followed by a much slower one, in agreement with earlier work on the decay of quantum turbulence created in thermal counterflow. Extrapolation of the initial fast decay suggests an initial line density, immediately following the expansion, of ∼107 cm−2. Smaller, but still substantial, vortex densities are also found to occur when the system is expanded from below the lambda transition, and the physical implications are discussed.

The temperature dependence of permittivity in MgO and Fe-MgO single crystals

The permittivities (ε′) of undoped MgO and iron-doped Fe-MgO single crystals have been measured over the temperature range 20 to 650‡ C for frequencies between 500 Hz and 50 kHz. From 25 to around 200‡ C the temperature dependence of ε′ fits well with Havingas formula and the value of [(ε′ − 1) (ε′ + 2)]−1 (∂ε′/∂T) = 1.02 × 10−2K−1 found for undoped MgO agrees closely with data published for lower temperature ranges; this increases considerably with the addition of iron, rising to 2.85×10−5K−1 for MgO single crystals doped with 12 900 p.p.m. iron. Above 200‡ C the permittivity changes much more rapidly than the Havinga formula predicts, the variation being greater in iron-doped specimens. The frequency dependence ofε′ is also temperature-dependent; below 200‡ Cε′ follows [ε′(Ω) − ε′∞] ∫Ω(n−1) withn=0.98±0.02 for all samples, but above 200‡ C the value ofε′ falls more rapidly with frequency than would be expected from this law. The effect is more pronounced for MgO with 12 900 p.p.m. iron. The results are discussed in terms of a contribution to the measured permittivity arising from temperature-enhanced conductivity.

The breakdown of superfluidity in liquid 4He. VI, Macroscopic quantum tunnelling by vortices in isotopically pure He II

Measurements are reported of the rate v at which negative ions nucleate quantized vortices in isotopically pure superfluid 4He for electric fields E, temperatures T and pressures P within the range 103 ⩽ E ⩽ 106 V m-1, 75 ⩽ T ⩽ 500 mK, 12 ⩽ P ⩽ 23 bar (= 2.3 MPa). The form of v(E, T) differs in unexpected ways from that observed in earlier work at higher P, exhibiting: a pronounced dip in v(T) at ca. 0.3 K whose depth and precise position depends on E and P ; an exponential increase in v(T) at higher T, with an activation energy considerably smaller than the roton energy gap; and distinct structure in v(E). The experimental data are discussed and analysed in terms of the macroscopic quantum tunnelling model proposed by Muirhead et al. (Phil. Trans. R. Soc. Lond. A 311, 433 (1984)). The relatively small barrier heights of ca. 2—3 K deduced from the data on this basis are construed as confirmation that the initial vortex is a loop rather than an encircling ring. The temperature dependence of v at low pressures is interpreted in terms of a phonon-driven vortex nucleation mechanism, and values for its cross section are extracted from the data. The minima in v(T) are ascribed to phonon damping of the tunnelling process, and the kinks observed in some of the low-temperature v(E) curves are attributed to tunnelling of the system into the first excited state of the nascent vortex loop.

A low-temperature high-sensitivity torsion balance magnetometer with in situ stator adjustment

Torsion balance magnetometry can be used as a versatile probe of two-dimensional electron systems. We have developed a highly sensitive magnetometer, utilizing capacitive proximity detection of the rotor position, for use at temperatures below 10 mK. The instrument incorporates two piezo-electric linear motors to enable the stator positions to be adjusted in situ at base temperature. The magnetometer responsivity is inversely proportional to the square of the rotor–stator separation and the novel linear motor technique, accompanied by effective vibration isolation and optimized capacitance bridge electronics, achieves a resolution 6.5×10−12 N m Hz−1/2. This resolution, together with the low temperatures attainable, allows for experiments that probe the family of quantum fluid states responsible for the fractional quantum Hall effect, even at filling factors greater than one.

Expansion of Liquid 4He Through the Lambda Transition

Zurek suggestedNature 317, 505; 1985) that the Kibble mechanism, through which topological defects such as cosmic strings are believed to have been created in the early Universe, can also result in the formation of topological defects in liquid4He, i.e. quantised vortices, during rapid quenches through the superfluid transition. Preliminary experiments (Hendry et al., Nature 368, 315; 1994) seemed to support this idea in that the quenches produced the predicted high vortex-densities. The present paper describes a new experiment incorporating a redesigned expansion cell that minimises vortex creation arising from conventional hydrodynamic flow. The post-quench line-densities of vorticity produced by the new cell are no more than 1010m−2, a value that is at least two orders of magnitude less than the theoretical prediction. We conclude that most of the vortices detected in the original experiment must have been created through conventional flow processes.

An appraisal of the noise performance of constant temperature bolometric detector systems

The noise and bandwidth behaviour of the constant temperature bolometer detector is analysed with a view to optimising practical systems. It is shown that careful adjustment of the time constants in this type of detector system is essential to avoid serious and unnecessary degradation of the attainable performance. It is concluded that a system with a critically damped response to a heat pulse input is optimal from the point of view of sensitivity and useful signal bandwidth. The use of feedback to enhance artificially the bandwidth of a sensor is considered but it is found that any attempt to compensate for a slow sensor element using this technique degrades the sensitivity seriously. Some general guidelines for the design of sensitive detector systems are suggested.

Quantum Evaporation from Superfluid 4He

The quantum evaporation experiments of Brown and Wyatt2have been re-analysed in the light of a recent measurement of the high-energy phonon spectrum created by a pulse-heated thin film10. Two sources of systematic error become significant at the level of the precision required by this new analysis: firstly, in the detector position which is recalibrated by using large-angle roton evaporation; and secondly, in the liquid height due to capillary action affecting the level-detectors. These effects have been included in an improved simulation of the experiment which has brought the angular dependence of the measured and theoretical phonon-atom evaporation results into agreement within the mechanical tolerances of the apparatus. The reanalysis suggests that the roton-atom evaporation probability increases with wave vector.

The influence of electrostatic fields on films of liquid helium

Prompted by the recent striking experimental results reported by Babkin and Hakonen that appeared to show that liquid helium-II does not wet magnesium fluoride, we have examined the effects that an inhomogeneous electrostatic field has on thin films of liquid helium at temperatures below 0.5K. Our model includes the influence of gravity, surface tension, the electric field and the van der Waals interaction between the helium and its supporting substrate. We show that, an inhomogeneous charge on the substrate can produce effects that mimic the surface profiles between wetted and non-wetted areas. The calculations also indicate that some special precautions may be necessary when studying films of liquid or solid helium on insulators.