Physical Review Letters

Binding of Impurities to a H4e Superfluid Vortex

Michael Sadd, Geoffrey V. Chester, Francesco Pederiva

Published Dec 20, 1999• 35 citations

Abstract

We calculate the binding energies of a ${}^{3}\mathrm{He}$ impurity and a fictitious ${}^{4}\mathrm{He}$ impurity to a superfluid ${}^{4}\mathrm{He}$ 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.

DOI: 10.1103/physrevlett.83.5310

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Physical Review Letters

Binding of Impurities to a H4e Superfluid Vortex

Michael Sadd, Geoffrey V. Chester, Francesco Pederiva

Published Dec 20, 1999• 35 citations

Publisher

Abstract

We calculate the binding energies of a

{}^{3}\mathrm{He}

impurity and a fictitious

{}^{4}\mathrm{He}

impurity to a superfluid

{}^{4}\mathrm{He}

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.

DOI: 10.1103/physrevlett.83.5310

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Micheal Sadd

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Vortex core states in superfluid Fermi-Fermi mixtures with unequal masses

M. Iskin

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 $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass $(^{6}\mathrm{Li})$ fermions and that the core density of the heavy-mass $(^{40}\mathrm{K})$ 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.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 $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass $(^{6}\mathrm{Li})$ fermions and that the core density of the heavy-mass $(^{40}\mathrm{K})$ 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.

arXiv:0804.1035Physical Review AAug 28, 200810 citations

We calculate the binding energies of a

{}^{3}\mathrm{He}

impurity and a fictitious

{}^{4}\mathrm{He}

impurity to a superfluid

{}^{4}\mathrm{He}

{\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.

\mathrm{dopant}+\mathrm{vortex}{+}^{4}{\mathrm{He}}_{{N}_{4}}

complex, which in a previous work [F. Dalfovo et al., Phys. Rev. Lett. 85, 1028 (2000)] was found to be energetically stable below a critical size

{N}_{\mathrm{cr}}

, is robust against the addition of

{}^{3}\mathrm{He}

. While

{}^{3}\mathrm{He}

atoms are distributed along the vortex line and on the surface of the

{}^{4}\mathrm{He}

drop, the impurity is mostly coated by

{}^{4}\mathrm{He}

atoms. Results for

{N}_{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}500

and a number of

{}^{3}\mathrm{He}

atoms ranging from 0 to 100 are presented, and the binding energy of the dopant to the vortex line is determined.

A method for calculating hydrodynamic added mass within the framework of time-dependent bosonic density functional theory (DFT) for superfluid

{}^{4}

He is developed. As a calibration of the model, it is shown to reproduce the classical hydrodynamic limit for purely repulsive interactions. To model real systems for which experimental data are available, the following ions were considered: Be

{}^{+}

, K

{}^{+}

, Ca

{}^{+}

, Sr

{}^{+}

, and Ba

{}^{+}

cations as well as the F${}^{\ensuremath{-}}$, Cl${}^{\ensuremath{-}}$, I${}^{\ensuremath{-}}$, and Br${}^{\ensuremath{-}}$ anions. The DFT model requires the ion-helium pair potential data as input, which were obtained from electron structure calculations by employing coupled clusters theory. The resultant static liquid density profiles as calculated by DFT were found to be in good agreement with previously published quantum Monte Carlo data. The calculated added masses for the positive ions correlated directly with the experimentally observed ion mobility data, by which the ions could be separated into two different categories based on the degree of the first solvent shell following the ion. The calculated added masses for the negative ions were found to be in disagreement with the existing experimental data, suggesting the possibility that other negatively charged species were observed in previous experiments. The negatively charged ions are predicted to have mobilities ($\ensuremath{\mu}$) within the range 0.8--1.0 cm

{}^{2}

V${}^{\ensuremath{-}1}$ s${}^{\ensuremath{-}1}$ in superfluid helium at 1.3 K with the order $\ensuremath{\mu}$(I${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(Br${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(Cl${}^{\ensuremath{-}}$)

>

$\ensuremath{\mu}$(F${}^{\ensuremath{-}}$).

The microscopic structure of a quantized vortex core in 2D

^{4}\mathrm{He}

is investigated using the fixed-phase approach. We present a general method to suggest new forms for the phase of a many-particle wave function. Starting from the Feynman phase, our scheme generates backflow corrections with qualitatively different properties than the starting Feynman vortex. We evaluate particle density, circulating current, core radius, and energy for an isolated vortex at zero temperature using Green's function Monte Carlo.

^{6}\mathrm{Li}

and

^{40}\mathrm{K}

atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass

(^{6}\mathrm{Li})

fermions and that the core density of the heavy-mass

(^{40}\mathrm{K})

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.