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arXiv:1109.4828 · Low Temperature Physics

On electric fields created by quantized vortices

A. S. Rukin, S. I. Shevchenko

Published Oct 1, 2011• 4 citations
arXivHTMLPDF

Abstract

It is shown that in a magnetic field the quantized vortices in a superfluid acquire a real quantized electric charge concentrated in the vortex core. This charge is compensated by an opposite surface charge, located at macroscopic distance from the vortex axis. It is found that polarization caused by the vortex velocity field does not give rise to electric fields outside an infinite cylinder. The vortex-created electric fields can be observed only near the cylinder end surfaces, which must be covered by dielectric covers in order to prevent leakage of the superfluid. The influence of cover properties on the vortex-created potential is studied here. The potentials created by vortices on point and ring electrodes are calculated.

DOI
10.1063/1.3671861

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It is shown that in a magnetic field the quantized vortices in a superfluid acquire a real quantized electric charge concentrated in the vortex core. This charge is compensated by an opposite surface charge, located at macroscopic distance from the vortex axis. It is found that polarization caused by the vortex velocity field does not give rise to electric fields outside an infinite cylinder. The vortex-created electric fields can be observed only near the cylinder end surfaces, which must be covered by dielectric covers in order to prevent leakage of the superfluid. The influence of cover properties on the vortex-created potential is studied here. The potentials created by vortices on point and ring electrodes are calculated.
It is shown that, in the presence of a magnetic field, a quantized vortex line in a superfluid liquid acquires a linear polarization charge, which is localized near the vortex axis over a length on the order of the coherence length. It is found that the total charge of a rectilinear vortex is nonzero, while the vortex pair and vortex ring have a nonzero dipole moment. The electric fields of rectilinear vortices near the end surface of a cylindrical vessel filled with a superfluid liquid are calculated. The electric polarization of superfluid systems in the presence of thermally activated vortex pairs and vortex rings has been studied. It is shown that such a polarization arises in the presence of relative motion of the normal and superfluid components.
In the article by Shevchenko and A. S. Rukin, Pis'ma v Zh. Eksp. Teor. Fiz. 90, 46 (2009), it has been found that quantized vortices in superfluid systems acquire a charge in a magnetic field. A compensating charge with the opposite sign on a surface of the system can be at a macroscopic distance apart from the charge of the vortex. It is shown that as a result the total energy of the vortex charge and the compensating charge can be negative in the presence of an inhomogeneous electric field, normal to a homogeneous magnetic field. The conditions under which this leads to the spontaneous emergence of quantized vortices in the system are found. A possibility to observe the effect in He II, Bose gases of alkali metals and systems with spatially indirect excitons is discussed.
A study is made of the electric polarization of quantized vortices in a superfluid Bose liquid and their interaction with electric field. Two types of vortex polarization are considered, both of which are due to the centrifugal forces exerted on the atoms of the liquid in their azimuthal motion around the vortex line. First, under the influence of these forces the atoms acquire dipole moments (inertial polarization in the absence of external field), and a nonuniform symmetric distribution of the polarization density arises around the vortex line. Here the vortex does not have an integral dipole moment, but each element of the vortex line possesses a quadrupole moment. Second, the centrifugal forces lead to a nonuniform distribution of the atomic density around the vortex line, and therefore the polarization density of the liquid in an external electric field is also nonuniform near the vortex line, and an individual element of the vortex line acquires an effective dipole moment proportional to the field (inductive polarization). Analytical expressions are obtained for the polarization density around rectilinear and ring-shaped vortex lines, and the effective dipole and quadrupole moments of such vortices are calculated. The distribution of ponderomotive forces acting on a superfluid liquid containing a quantized vortex in an electric field is analyzed, and the corrections to the vortex energy due to the field are found. Numerical estimates of these effects are made for the case of HeII.
We show that an ion carried through an electric field by a quantized vortex ring in helium II will cause a symmetric change in the radius of the ring, even though the ion is located asymmetrically on the core of the vortex ring. The localized force on the ion will combine with a specific series of vortex waves to give a uniform growth of the ring with a small component of drift velocity perpendicular to the applied electric field. This type of energy transfer may also play an important role in superfluid turbulence. Our calculations should be valid for localized forces on thin-core classical vortices as well.
The Meissner effect is a hallmark of superconductivity arising from the interplay between charged superfluids and electromagnetic fields. However, superfluidity can also occur in systems of charge-neutral particles with magnetic or electric dipole moments, such as Bose-Einstein condensates of magnons or excitons. Despite this interest, the electromagnetic response of dipole superfluids, including potential analogues or contrasts to the Meissner effect, remains poorly understood. Here we develop a Ginzburg-Landau theory to describe dipole superfluids subjected to a pseudo-magnetic field, which is induced by a spatially modulating electromagnetic field. In magnetic dipole superfluids, the response differs strikingly from the conventional Meissner effect: the external field is enhanced by a positive feedback, forming a vortex lattice separated by singular domain walls with diverging electric charges. In contrast, electric dipole superfluids exhibit screening akin to superconductors, where the pseudo-magnetic field is suppressed except near vortices. The electromagnetic response of dipole superfluids, including potential analogues to the Meissner effect, remains poorly understood. This paper develops a phenomenological theory and shows that magnetic-dipole superfluids form vortex lattices separated by singular domain walls with concentrated electric charge, while electric-dipole superfluids exhibit vortex lattices resembling those in conventional superconductors.