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Physical Review Letters

Dynamics with a Non-Newtonian Gas: The Force on a Body Moving through a Beam of Excitations in Superfluid 3 He

D. J. Cousins, M. P. Enrico, S. N. Fisher, G. R. Pickett, N. S. Shaw

Published Sep 22, 1997• 45 citations
Publisher

Abstract

The excitation gas in superfluid ${}^{3}$He-B is unique in having a completely non-Newtonian dispersion relation and being free and accessible to dynamic experiment. The dynamics of this excitation gas are very interesting and highly nonintuitive. In the present experiment we show that in a thermal beam of such excitations, generated by a quasiparticle blackbody radiator, the force exerted on a macroscopic moving object is very large but, more importantly, highly insensitive to the relative direction of the excitation beam and the velocity of the object.

DOI
10.1103/physrevlett.79.2285

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The excitation gas in superfluid 3{}^{3}3He-B is unique in having a completely non-Newtonian dispersion relation and being free and accessible to dynamic experiment. The dynamics of this excitation gas are very interesting and highly nonintuitive. In the present experiment we show that in a thermal beam of such excitations, generated by a quasiparticle blackbody radiator, the force exerted on a macroscopic moving object is very large but, more importantly, highly insensitive to the relative direction of the excitation beam and the velocity of the object.
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.
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.
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 consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.
We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity vL{v}_{L}vL​. The expectation has been that vL{v}_{L}vL​ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid 3He^{3}\mathrm{He}3He. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds vL{v}_{L}vL​. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than vL{v}_{L}vL​ and the drag force (per cross-sectional area) at 2vL2{v}_{L}2vL​ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below vL{v}_{L}vL​.