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Low Temperature Physics

Magnetic polarization of quantum vortices in He II

В. Д. Нацик

Published Jul 1, 2008• 17 citations
Publisher

Abstract

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.

DOI
10.1063/1.2956999

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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.
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 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.
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
We present the analysis of the structure of fermionic vortices with the spin-polarized core from a weak coupling limit to the unitary regime. We show the mechanism for the generation of the reversed circulation in the vortex core induced by an excess of majority spin particles. We introduce the classification of the polarized vortices based on the number of Fermi circles where the minigap vanishes. This provides a unique description of the vortex as one cannot smoothly map wave functions into one another corresponding to vortices differing by the number of Fermi circles. The effective mass of quasiparticles along the vortex core is analyzed and its role in the propagation of spin-polarization along the vortex line is discussed.