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Physical Review Letters

Scattering of first sound by superfluid vortices

Caroline Nore, Marc Brächet, E. Cerda, E. Tirapegui

Published Apr 18, 1994• 26 citations
Publisher

Abstract

The simplest interaction between sound and quantized superfluid vortices is investigated both analytically in the Born approximation and numerically, using the nonlinear Schr\"odinger equation. Compared with the scattering by a classical vortex, the quantum result reflects the structure of the vortex core and has an extra phase shift. The order of magnitude of the effects suggests possible experiments in rotating superfluid helium.

DOI
10.1103/physrevlett.72.2593

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The simplest interaction between sound and quantized superfluid vortices is investigated both analytically in the Born approximation and numerically, using the nonlinear Schr"odinger equation. Compared with the scattering by a classical vortex, the quantum result reflects the structure of the vortex core and has an extra phase shift. The order of magnitude of the effects suggests possible experiments in rotating superfluid helium.
Abstract Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases. In this work, we develop methods to compute both the vortex and sound flow fields in an arbitrary two-dimensional domain. Further, we analyse the dispersive interaction of vortices with sound modes in a two-dimensional superfluid and develop a model that quantifies this interaction for any vortex distribution on any two-dimensional bounded domain, possibly non-simply connected, exploiting analogies with fluid dynamics of an ideal gas and electrostatics. As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.
We study inelastic interactions of particles with quantized vortices in superfluids by using a semiclassical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon-doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different energies and impact parameters of incident particles are considered. We show that inelastic scattering is closely linked to the generation of Kelvin waves along a quantized vortex during the interaction even if there is no capture. The capture criterion of an impurity is formulated in terms of the binding energy.
We propose a hydrodynamic analog of the Aharonov-Bohm experiment in which second-sound waves are scattered on a quantized vortex in superfluid helium. The time lag that develops between the two sides of a second-sound plane wave impinging on a vortex from the side would be compared. Estimates for these experiments show that for reasonable experimental conditions the wavefront splitting can be readily measured at reduced temperatures of 10 −6 . The advantages of doing this experiment near the superfluid transition is discussed. This experiment would compliment the three other Aharonov-Bohm–type experiments which involve all four possible combinations of classical/quantum waves and classical/quantum vortices. This technique would provide a non-invasive means of investigating the dynamics of quantum vortex nucleation and their stability as well as addressing the problem of multiply quantized.
Quantum vortices are pivotal for understanding of phenomena in quantum hydrodynamics. Vortices were observed in different physical systems like trapped dilute Bose-Einstein condensates, liquid helium, exciton-polariton condensates and other types of systems. Foreign particles attached to the vortices often serve for a visualization of the vortex shape and kinematics in superfluid experiments. Fascinating discoveries were made in the field of cold quantum mixtures, where vortices created in one component may interact with the other component. This works raise the fundamental question of the interaction between quantum vortices and matter. The generalized nonlinear Schrodinger equation based formalism is applied here to model three different processes involving the interaction of quantum vortices with foreign particles: propagation of a fast classical particle in a superfluid under the influence of sound waves, scattering of a single fermion by a quantized vortex line and dynamics of vortex pairs doped with heavy bosonic matter. The obtained results allow to to clarify the details of recent experiments and acquire a better understanding of the multicomponent quantum turbulence.
Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin-vortex molecules into elementary half-vortices, when seeding opposite vorticity between the two spinorial components. Remarkably, we also observe that vortices placed in close proximity experience a pull-push scenario leading to unusual scattering-like events that can be described by a tunable effective potential. Understanding vortex interactions can be useful in quantum hydrodynamics and in the development of vortex-based lattices, gyroscopes, and logic devices.
We introduce a nonlinear Schr\"odinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where $a{n}^{1/3}\ensuremath{\ll}1$ with aaa the interatomic s\mathit{s}s-wave scattering length and nnn the bosonic density, to the unitarity limit, where $a\ensuremath{\rightarrow}+\ensuremath{\infty}$. We call this equation the unitarity Schr\"odinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.