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Probing Bogoliubov Quasiparticles in Superfluid $$^3$$ 3 He with a ‘Vibrating-Wire Like’ MEMS Device

Martial Defoort, Sébastien Dufresnes, S. L. Ahlstrom, D. I. Bradley, R. P. Haley, A. M. Guénault, E. A. Guise, G. R. Pickett, Poole, M., Andrew Woods, V. Tsepelin, S. N. Fisher, Henri Godfrin, Eddy Collin

Published May 1, 2016• 16 citations
OpenAlex

Abstract

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.

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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.

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Quasiparticle beam profile measurements in superfluid helium 3 - B

S. L. Ahlstrom

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.

•Nov 18, 2016•0 citations

Quasiparticle dynamics in superfluid 3He

G. R. Pickett, A. M. Guénault

Excitations in many areas of condensed matter physics have dispersion relations which are very unlike those of simple newtonian objects. An unusual energy-momentum relation should lead to unconventional dynamics. Unfortunately most excitations are trapped in lattices or are otherwise inaccessible. One place where dynamic experiments are possible is in the superfluids, since here the excitations propagate freely in the superfluid condensate which we can regard as a mechanical vacuum. We can now cool superfluid 3He to a temperature where the excitation mean free paths are long enough for dynamic experiments to be feasible, which implies temperatures of the order of 100μK. Since the dispersion relation is tied to the rest frame of the condensate, it will be distorted by condensate motion, providing us with a way of influencing the dispersion curve. For example, a container of superfluid with a velocity gradient will have a range of excitation dispersion curves depending on the local velocity of the condensate. This means that the density of states available to the excitations will vary with position. We discuss the dynamical implications of this in terms of the behaviour of a vibrating wire resonator in the liquid, which shows unusual and often counter-intuitive behaviour. Among other things, for example, at a low enough temperature the force on a moving object in the excitation gas becomes independent of the velocity.

Physica Scripta•Jan 1, 1991•0 citations
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.
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.
The resistance to motion of a wire in superfluid 3B^{3}\mathit{B}3B has three contributions: that due to the internal friction of the resonator; that due to pair breaking; and that due to the quasiparticle gas. We have been able to separate quasiparticle contribution and find that it is highly nonlinear with velocity on the scale of the Landau velocity, \ensuremath{\Delta}/pF{\mathrm{p}}_{\mathrm{F}}pF​, and falls with increasing velocity. This indicates that the quasiparticle resistance is also governed by the condensate, almost certainly through Andreev reflection in the flow field around the wire.
Drag on Cylinders Moving in Superfluid 3^33He-B as the Dimension Spans the Coherence Length
Abstract Vibrating probes when immersed in a fluid can provide powerful tools for characterising the surrounding medium. In superfluid 3^33 3 He-B, a condensate of Cooper pairs, the dissipation arising from the scattering of quasiparticle excitations from a mechanical oscillator provides the basis of extremely sensitive thermometry and bolometry at sub-millikelvin temperatures. The unique properties of the Andreev reflection process in this condensate also assist by providing a significantly enhanced dissipation. While existing models for such damping on an oscillating cylinder have been verified experimentally, they are valid only for flows with scales much greater than the coherence length of 3^33 3 He, which is of the order of a hundred nanometres. With our increasing proficiency in fabricating nanosized oscillators, which can be readily used in this superfluid, there is a pressing need for the development of new models that account for the modification of the flow around these smaller oscillators. Here we report preliminary results on measurements of the damping in superfluid 3^33 3 He-B of a range of cylindrical nanosized oscillators with radii comparable to the coherence length and outline a model for calculating the associated drag.
Using a simple one-dimensional model, we show that the existence of the energy gap for excitations in an isotropic BCS superfluid leads to strongly nonlinear mechanical behavior of the liquid in the ballistic quasiparticle limit. The nonlinear damping of a vibrating wire in 3B^{3}\mathit{B}3B below 200 \ensuremath{\mu}K is explained, both in its velocity dependence and magnitude. At modest velocities (\ensuremath{\upsilon}>kT/pF{\mathrm{p}}_{\mathrm{F}}pF​), the damping force on an object moving through the superfluid becomes independent of velocity, an unexpected result with several interesting implications.
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.
Excitations in many areas of condensed matter physics have dispersion relations which are very unlike those of simple newtonian objects. An unusual energy-momentum relation should lead to unconventional dynamics. Unfortunately most excitations are trapped in lattices or are otherwise inaccessible. One place where dynamic experiments are possible is in the superfluids, since here the excitations propagate freely in the superfluid condensate which we can regard as a mechanical vacuum. We can now cool superfluid 3He to a temperature where the excitation mean free paths are long enough for dynamic experiments to be feasible, which implies temperatures of the order of 100μK. Since the dispersion relation is tied to the rest frame of the condensate, it will be distorted by condensate motion, providing us with a way of influencing the dispersion curve. For example, a container of superfluid with a velocity gradient will have a range of excitation dispersion curves depending on the local velocity of the condensate. This means that the density of states available to the excitations will vary with position. We discuss the dynamical implications of this in terms of the behaviour of a vibrating wire resonator in the liquid, which shows unusual and often counter-intuitive behaviour. Among other things, for example, at a low enough temperature the force on a moving object in the excitation gas becomes independent of the velocity.