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Journal of the Physical Society of Japan

Mobility of Ions Trapped Below a Free Surface of Superfluid 3He

Hiroki Ikegami, Suk Bum Chung, Kimitoshi Kōno

Published Nov 20, 2013• 18 citations
Publisher

Abstract

The \(p\)-wave superfluid phases of 3He-B and 3He-A are topologically nontrivial. Topological properties manifest themselves as the formation of bound states at a surface. Unusual properties of the \(p\)-wave superfluids also appear around impurities, such as an ion immersed in liquid 3He. In this article, we present the mobility of positive and negative ions trapped below a free surface of 3He-B and 3He-A measured down to 250 μK, which is much lower than the temperatures attained in previous experiments in the bulk. Mobility measurements are conducted for two purposes: one is to figure out details of the scattering of a quasiparticle by an impurity in \(p\)-wave superfluids, and the other is to detect the surface Andreev bound states (SABSs) at a free surface of 3He-B formed as a result of the nontrivial topology of 3He-B. We find, in both superfluid phases, that the mobility shows a considerable increase with decreasing temperature. In both superfluid phases, the mobility of a negative ion at high temperatures is in agreement with the theory for the bulk, in which the \(p\)-wave coherence in a Bogoliubov quasiparticle upon scattering is taken into account. This agreement demonstrates a crucial role of the \(p\)-wave coherence in scattering. The mobility at low temperatures deviates from the theory, particularly in 3He-B, and the possible origins of the deviation are discussed. The mobility of a positive ion, by contrast, does not follow the theory that includes the \(p\)-wave coherence, in both 3He-B and 3He-A. In 3He-B, the mobility of both negative and positive ions remarkably shows no dependence on the depth of the ions even if the depth is varied over the coherence length. The lack of depth dependence indicates that SABSs have little contribution to the momentum transfer rate of the ions, which might reflect the unusual Majorana aspect of SABSs.

DOI
10.7566/jpsj.82.124607

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The (p)-wave superfluid phases of 3He-B and 3He-A are topologically nontrivial. Topological properties manifest themselves as the formation of bound states at a surface. Unusual properties of the (p)-wave superfluids also appear around impurities, such as an ion immersed in liquid 3He. In this article, we present the mobility of positive and negative ions trapped below a free surface of 3He-B and 3He-A measured down to 250 μK, which is much lower than the temperatures attained in previous experiments in the bulk. Mobility measurements are conducted for two purposes: one is to figure out details of the scattering of a quasiparticle by an impurity in (p)-wave superfluids, and the other is to detect the surface Andreev bound states (SABSs) at a free surface of 3He-B formed as a result of the nontrivial topology of 3He-B. We find, in both superfluid phases, that the mobility shows a considerable increase with decreasing temperature. In both superfluid phases, the mobility of a negative ion at high temperatures is in agreement with the theory for the bulk, in which the (p)-wave coherence in a Bogoliubov quasiparticle upon scattering is taken into account. This agreement demonstrates a crucial role of the (p)-wave coherence in scattering. The mobility at low temperatures deviates from the theory, particularly in 3He-B, and the possible origins of the deviation are discussed. The mobility of a positive ion, by contrast, does not follow the theory that includes the (p)-wave coherence, in both 3He-B and 3He-A. In 3He-B, the mobility of both negative and positive ions remarkably shows no dependence on the depth of the ions even if the depth is varied over the coherence length. The lack of depth dependence indicates that SABSs have little contribution to the momentum transfer rate of the ions, which might reflect the unusual Majorana aspect of SABSs.
This article reviews recent experimental and theoretical work on the mobility of negative ions in the superfluid A and B phases of liquid 3He. In the normal Fermi liquid at temperatures below ∼ 50 mK and also in the superfluid close to the superfluid transition temperature, Tc , the mobility of a negative ion may simply be considered as limited by the elastic scattering of 3He quasiparticles. This explains the constancy of the ion mobility in the normal phase. However, underlying the rapid increase of the measured mobility in the superfluid phases there is a subtle quantum-mechanical scattering effect. Detailed solutions of the 3He quasiparticle—negative ion scattering process in the pair-correlated state provide a simple physical picture of an energy-dependent forward-peaking phenomenon. This yields quantitative theoretical results for the ion mobility in the quasi-isotropic B phase and for the ion mobility tensor in the anisotropic A phase which agree with the experimental data.
The mobility of negative ions trapped on linear vortices in rotating superfluid helium has been measured by a time-of-flight technique in the temperature range $0.8\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<1.6\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. Measurements could not be extended below 0.8\ifmmode^\circ\else\textdegree\fi{}K because, contrary to the present theory, the ion escape rate became too large. No evidence of direct trapping of positive ions by vortex lines was observed down to 0.4\ifmmode^\circ\else\textdegree\fi{}K. The trapped-ion mobility is interpreted in terms of scattering of the ion by thermal distributions of quantized vortex waves and rotons localized about the vortex axis.
Abstract The B phase of superfluid 3He can be cooled into the pure superfluid regime, where the thermal quasiparticle density is negligible. The bulk superfluid is surrounded by a quantum well at the boundaries of the container, confining a sea of quasiparticles with energies below that of those in the bulk. We can create a non-equilibrium distribution of these states within the quantum well and observe the dynamics of their motion indirectly. Here we show that the induced quasiparticle currents flow diffusively in the two-dimensional system. Combining this with a direct measurement of energy conservation, we conclude that the bulk superfluid 3He is effectively surrounded by an independent two-dimensional superfluid, which is isolated from the bulk superfluid but which readily interacts with mechanical probes. Our work shows that this two-dimensional quantum condensate and the dynamics of the surface bound states are experimentally accessible, opening the possibility of engineering two-dimensional quantum condensates of arbitrary topology.
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.