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Physica B Condensed Matter

The binding of 3He impurities to a superfluid vortex

Micheal Sadd

Published Jul 1, 2000• 0 citations
Publisher

Abstract

Using many-body wave functions we have calculated the binding energies of a 3He impurity and a fictitious 4He impurity to a superfluid vortex. We use both a shadow wave function with distributed vorticity, ΨD, and the Onsagar–Feynman function with singular vorticity, ΨO−F. For both wave functions there was no difference in the binding energies of the mass 3 and mass 4 impurities. The binding energy was independent of the density for ΨD, but strongly density dependent for ΨO−F. The value of 2.3 K for ΨD, is somewhat smaller than the experimental estimate. Our results strongly suggest that the binding is due to the displacement of high-velocity 4He atoms from the vortex core by the impurity.

DOI
10.1016/s0921-4526(99)02675-7

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Using many-body wave functions we have calculated the binding energies of a 3He impurity and a fictitious 4He impurity to a superfluid vortex. We use both a shadow wave function with distributed vorticity, ΨD, and the Onsagar–Feynman function with singular vorticity, ΨO−F. For both wave functions there was no difference in the binding energies of the mass 3 and mass 4 impurities. The binding energy was independent of the density for ΨD, but strongly density dependent for ΨO−F. The value of 2.3 K for ΨD, is somewhat smaller than the experimental estimate. Our results strongly suggest that the binding is due to the displacement of high-velocity 4He atoms from the vortex core by the impurity.
We calculate the binding energies of a 3He{}^{3}\mathrm{He}3He impurity and a fictitious 4He{}^{4}\mathrm{He}4He impurity to a superfluid 4He{}^{4}\mathrm{He}4He vortex. Within the accuracy of the calculation, there is no difference between the mass-3 and mass-4 binding energies, suggesting that the binding is due to the displacement of atoms from the core. Comparing the results between Onsager-Feynman ( ${\ensuremath{\Psi}}_{\mathrm{OF}}$) and ``shadow'' ( ${\ensuremath{\Psi}}_{D}$) variational functions, the energy is dependent on the density for ${\ensuremath{\Psi}}_{\mathrm{OF}}$, but independent for ${\ensuremath{\Psi}}_{D}$. The binding of 2.3 K for ${\ensuremath{\Psi}}_{D}$ at zero pressure is smaller than the experimental estimate. We also estimate the binding energies of charged ions.
We analyze the vortex core states of two-species (mass imbalanced) superfluid fermion mixtures as a function of two-body binding energy in two dimensions. In particular, we solve the Bogoliubov--de Gennes equations for a population balanced mixture of 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass (6Li)(^{6}\mathrm{Li})(6Li) fermions and that the core density of the heavy-mass (40K)(^{40}\mathrm{K})(40K) fermions is highly depleted. This is in contrast with the one-species (mass balanced) mixtures with balanced populations where an equal amount of density depletion is found at the vortex core for both pseudospin components.
A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological models.
Model many-body wave functions are constructed for a quantized vortex line and ring. The corresponding variational energies are calculated using an approximate integral equation derived by Percus and Yevick for classical fluids. The energy of the line is close to that found in the Hartree theory. However, the density distribution in the core region is markedly different, and the core size is somewhat smaller, being of the order of 1 \AA{}. The velocity of translation of the vortex ring is calculated by a new method, and excellent agreement is obtained with the experimental results of Rayfield and Reif. The condensed-state wave function is computed numerically, and it is found that in the core of the vortex there are about 20% fewer particles in the condensed state than in the zero-momentum state when the system is in equilibrium.
We calculate the overlap between two many-body wave functions for a superfluid film containing a vortex at shifted positions. Comparing the results to phenomenological theories, which treat vortices as point particles, we find that the results are consistent if the point-particle vortices are considered as under the action of the Magnus force and in weak interaction with sound waves of the superfluid. We are then able to resolve the disagreement concerning the effective mass of vortices, showing it is finite.
Structure and energy of a superfluid vortex line and a neutral impurity (He3) trapped by it are investigated in the Hartree-Fock approximation. In dilute gas the shape of the impurity is prolate along the vortex line, while in dense gas it becomes more spherical. In liquid helium the ratio of the axes is estimated at √0.842 and the binding energy at 3.5°K. A rough estimate of the saturation density is given. It is pointed out that at this density the tension has decreased to 60% of that in pure He4.