On the dipole moment of quantized vortices generated by flows

TL;DR

This paper demonstrates that quantized vortices in superfluid films generate an electric dipole moment, which depends on the flow velocity and vortex circulation, linking vortex dynamics to electric polarization.

Contribution

It introduces a theoretical framework connecting vortex-induced polarization and electric dipole moments in superfluid systems, highlighting the dependence on flow and vortex properties.

Findings

Vortices create an electric potential resembling a dipole.

The dipole moment depends on flow velocity and vortex circulation.

Superfluid vortices can be characterized by an electric dipole moment.

Abstract

The polarization charge $\rho $ of an inhomogeneous superfluid system is expressed as a function of the order parameter $\Phi ({{\mathbf{r}}_{1}},{{\mathbf{r}}_{2}})$. It is shown that if the order parameter changes on macroscopic distances, the polarization charge ${{\rho }_{pol}}$ is proportional to $A{{\nabla }^{2}}n$, and the polarization $\mathbf{P}$ is proportional to $A\nabla n$, where $n$ is the density of the system. For noninteracting atoms the proportionality coefficient $A$ is independent of density, and in the presence of interaction $A$ is proportional to $n$. The change of the Bose gas density is found in the presence of a flow $\mathbf{w}={{\mathbf{v}}_{n}}-{{\mathbf{v}}_{s}}$ passing the vortex. It is found that a vortex in a superfluid film creates an electric potential above the film. This potential has the form of a potential of a dipole, allowing to assign a dipole moment to the vortex. The dipole moment is a sum of two terms, the first one is proportional to the relative flow velocity $\mathbf{w}$ and the second one is proportional to $\left[ \mathbf{\kappa }\times \mathbf{w} \right]$, where $\mathbf{\kappa }$ is the vortex circulation.