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Quasiparticle beam profile measurements in superfluid helium 3 - B

S. L. Ahlstrom

Published Nov 18, 2016• 0 citations
OpenAlex

Abstract

This thesis details experiments in the ballistic regime of superfluid 3He-B at temperatures around 100 ➭K. In this thesis, the quasiparticle beam profile from a Black-Body radiator and a vibrating wire resonator is measured using a quasiparticle camera which consists of 25 tuning forks. The vibrating wire resonator is found to have a very thinly spread beam at velocities slightly higher than the pair-breaking critical velocity which spreads out at higher velocities. At 21 mm/s the vibrating resonator is found to have a more focused beam than the Black-Body radiator where both beam profiles are found to be focused around the centre of the quasiparticle camera. A theoretical model is created in order to model the spread and intensity of the experimental beam profile from the Black-Body radiator. In this thesis, the response of some of the probes to thermal damping is measured in the form of the geometrical constants γ and λ. The geometrical constant λ is related to the velocity dependence of the probe to thermal damping and is found for two wires of varying diameter, a tuning fork and its overtone mode in which all the values of λ were close to unity. The geometrical constant γ is related to the sensitivity of a probe to thermal damping. This is found for a Black-Body radiator and then used to derive the sensitivity for other wires in the cell in thermal equilibrium with it. Two resonant modes of a small tuning fork are used to do a Black-Body radiator calibration on the area around the tuning fork which is used to find the sensitivity of 25 tuning forks (pixels) in the quasiparticle camera.

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This thesis details experiments in the ballistic regime of superfluid 3He-B at temperatures around 100 ➭K. In this thesis, the quasiparticle beam profile from a Black-Body radiator and a vibrating wire resonator is measured using a quasiparticle camera which consists of 25 tuning forks. The vibrating wire resonator is found to have a very thinly spread beam at velocities slightly higher than the pair-breaking critical velocity which spreads out at higher velocities. At 21 mm/s the vibrating resonator is found to have a more focused beam than the Black-Body radiator where both beam profiles are found to be focused around the centre of the quasiparticle camera. A theoretical model is created in order to model the spread and intensity of the experimental beam profile from the Black-Body radiator. In this thesis, the response of some of the probes to thermal damping is measured in the form of the geometrical constants γ and λ. The geometrical constant λ is related to the velocity dependence of the probe to thermal damping and is found for two wires of varying diameter, a tuning fork and its overtone mode in which all the values of λ were close to unity. The geometrical constant γ is related to the sensitivity of a probe to thermal damping. This is found for a Black-Body radiator and then used to derive the sensitivity for other wires in the cell in thermal equilibrium with it. Two resonant modes of a small tuning fork are used to do a Black-Body radiator calibration on the area around the tuning fork which is used to find the sensitivity of 25 tuning forks (pixels) in the quasiparticle camera.
In this thesis we use quartz tuning fork resonators to probe properties of normal and superfluid 4He and 3He. Our main goal is to study both quantum turbulence and acoustic emission of tuning forks in liquid helium. By employing a multi-frequency lock-in amplifier we contrast single and multi- frequency methods of measuring tuning forks in the linear regime. In the non-linear response of tuning forks during turbulence we create multi-frequency excitations called intermodulation products which are used to find the non-linear forces that created them. We apply this technique to quantum turbulence in superfluid 4He-II and find that the retarding in-phase force on the fork increases at a critical velocity for turbulence nucleation. We also observe that the out-of-phase non-linear force increases, which we attribute to energy loss via vortex ring emission by the fork. Superfluid 3He is a fermionic condensate of Cooper pairs of 3He atoms. At ultra-low temperatures of 120 μK thermally excited unpaired quasiparticles travel ballistically through the condensate. We beam quasiparticles from a black body source towards a 5 × 5-pixel camera and observe that the excitations follow photonic-like trajectories. We apply the source-camera configuration to non-invasively detect and even image quantum vortices, that are topological defects in the superfluid. Lastly, we explore the frequency dependent damping of quartz tuning forks in liquid 3He. We find that at high frequencies the fork damping is governed by acoustic emission. Furthermore, we show that existing models developed for sound emission in 4He can be used to predict observed acoustic damping in 3He. The results also suggest that devices for 3He experiments should be placed in cavities or designed to operate at low frequencies.
This thesis describes experiments conducted on B phase 3He in the μK temperature regime to investigate the turbulent properties of quantised vortices created by driving a vibrating wire resonator above its superfluid pair breaking critical velocity. By operating several resonators as highly sensitive vortex detectors the localised effects of vortex lines have been measured. The results have shown the vortices being of greater density in the directions of the generating wire motion and the rate of production being dependent upon the generator wire velocity. The rate at which the vortices decay spatially has been shown to approximate to a simple exponential and the decay length of this exponential has been measured. Using a thermal quasiparticle beam emitted by a black body radiator, the temperature dependence of the vorticity has been investigated for several quasiparticle beam temperatures between 177μK and 275μK and several bulk superfluid temperatures between 171μK and 236μK. The vortex line density of the turbulence has been calculated using a mathematical model developed here at Lancaster and shows some dependence on the temperature of the superfluid. The method of using a quasiparticle beam emitted from a black body radiator may be developed to allow a higher resolution of investigation of vortex creation and decay.
Quantum turbulence is a conceptually simple form of turbulence, consisting of a tangle of quantised vortex lines. It provides a model system, through which it may be possible to understand features of the complex and not yet fully understood classical turbulence. A novel detector made from arrays of custom-designed tuning forks was developed and used to investigate properties of excitation beams and quantum turbulence in superfluid 3He-B at temperatures below 200 µK. The detector was constructed from 5 arrays of 5 tuning forks mounted in a copper block to create a 25 pixel square detector of excitation flux. The detector was situated in a cell such that it could be illuminated with a beam of thermal excitations, and that turbulence could be generated in the path of the beam, which will cast a shadow on the face. Characterisation of the detector response to beams generated by the black-body radiator and source wire were performed. We observe that the beam generated by a black-body radiator appears approximately symmetric, consistent with being emitted from a point-source of excitations. In addition to this we find that the profile of the beam generated by the black-body radiator was independent of the power applied to it, an important assumption of the properties of the black-body radiator that had not been previously observed. The beam emitted from a vibrating wire was found to be much narrower and has a angular profile that changes as the velocity of the wire is increased. Probing a turbulent tangle generated by a vibrating wire with this beam showed that the turbulence appears to fill all of the volume in between the radiator and detector. The vortex line density of the tangle appeared the be greatest in the vicinity of the wire, consistent with previous measurements of the vortex tangle generated by vibrating wires. In addition, we find that there are reproducible features in the development of the shadow as a function of the wire velocity, indicating that there is some structure in the development. The shadow is independent of the power of the beam used to probe the tangle. Measurements of fluctuations in the shadow cast by the vortex tangle show that the turbulence has a spectrum reminiscent of the Kolmogorov spectrum. In addition to this the resolution of the detector is such that it is possible in principle to measure the shadow cast by a single vortex line, and we examine candidate events for such a measurement. This represents the first such measurement of the motion of vortex lines in 3He-B.
Using a new quasiparticle detector and source consisting of a blackbody radiator, we have made the first measurements of the divergence of a beam of quasiparticles produced by a vibrating-wire resonator moving at supercritical velocities in superfluid 3B^{3}\mathit{B}3B at the zero-temperature limit. At velocities just above the critical velocity of \ensuremath{\Delta}/3pF{\mathit{p}}_{\mathit{F}}pF​ we see a very narrow beam directed along the direction of motion of the wire. As the maximum wire velocity increases the beam spreads to saturate at a half-angle divergence of approximately 55\ifmmode^\circ\else\textdegree\fi{} at a maximum velocity of order \ensuremath{\Delta}/pF{\mathit{p}}_{\mathit{F}}pF​.
We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid 3 He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.
Probing Bogoliubov Quasiparticles in Superfluid 3^33 3 He with a ‘Vibrating-Wire Like’ MEMS Device
We have measured the interaction between superfluid 3He–B and a micro-machined goalpost-shaped device at temperatures below 0.2Tc. The measured damping follows well the theory developed for vibrating wires, in which the Andreev reflection of quasiparticles in the flow field around the moving structure leads to a nonlinear frictional force. At low velocities, the damping force is proportional to velocity, while it tends to saturate for larger excitations. Above a velocity of 2.6 mm s−1, the damping abruptly increases, which is interpreted in terms of Cooper-pair breaking. Interestingly, this critical velocity is significantly lower than that reported with other mechanical probes immersed in superfluid 3He. Furthermore, we report on a nonlinear resonance shape for large motion amplitudes that we interpret as an inertial effect due to quasiparticle friction, but other mechanisms could possibly be invoked as well.