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arXiv:2303.03780 · Low Temperature Physics

On the electric charge of quantized vortices and the dipole moment of vortex pairs and rings in a magnetic field

Aleksandr Konstantinov, S. I. Shevchenko

Published Jun 1, 2023• 0 citations
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Abstract

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.

DOI
10.1063/10.0019427

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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.
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.
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.
The weak magnetic polarization which a quantum vortex in a superfluid Bose liquid acquires as a result of the mutual electric polarization of atoms and the nonuniform distribution of the atomic density in its core is discussed. A rectilinear single-quantum vortex carries a magnetic moment directed along and proportional to the length of the vortex line. The magnetic moment density per unit length and the corresponding quantum of magnetic flux (vortex fluxoid) are directly related with the quantum circulation of the superfluid flow in the vortex. Numerical estimates of this effect are presented for vortices in He II.
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.
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.