Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0210526 · Physical Review Letters

Microscopic Structure of a Vortex Line in a Dilute Superfluid Fermi Gas

Nicolai Gayle Nygaard, Georg M. Bruun, Charles W. Clark, David L. Feder

Published May 30, 2003• 50 citations
arXivHTMLPDF

Abstract

The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.

DOI
10.1103/physrevlett.90.210402

Related papers

Vortex line in a neutral finite-temperature superfluid Fermi gas

Nicolai Gayle Nygaard, Georg M. Bruun, Barry I. Schneider +2 more

The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov--de Gennes theory. Various thermodynamic properties are calculated, and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied, and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.

arXiv:cond-mat/0312258•Physical Review A•May 20, 2004•19 citations

Superfluidity in a Degenerate Atomic Fermi Gas

Nicolai Gayle Nygaard

Dilute atomic gases have become a powerful tool for studying many-body quantum mechanics. The best example of this is the achievement of Bose-Einstein condensation in 1995 in a gas of Bose atoms, a discovery which has invoked a confluence of ideas from condensed matter, atomic and nuclear physics. Now a concerted research effort is focused on creating and studying a BCS superfluid in an atomic Fermi gas. In the work presented here we study in detail pairing superfluidity in a Fermi gas of atoms, by self-consistently solving the Bogoliubov-de Gennes equations, both for bulk systems, and for atoms in a harmonic confining potential. A critical part of this work is the derivation of a regularized theory, which is formulated entirely in terms of physically measurable quantities, such that a quantitative comparison between theory and experiment is possible with no adjustable parameters. The resulting equations form a non-linear problem, and the accurate numerical solution of this poses a formidable challenge. A major component of this thesis is the development of efficient computational approaches to overcome these difficulties. Based on the linear response of the gas to a twisting of the order parameter phase, the superfluid density can be defined as a generalized elasticity of the system. Using finite temperature perturbation theory we calculate the superfluid density in an inhomogeneous system. We investigate the structure and thermodynamic properties of a singly quantized vortex line in a gas of superfluid fermionic atoms, making the first quantitative determination the critical rotation frequency for thermodynamic stability of the vortex state, and study the nature of the bound states in the vortex core. These excitations fill the core, making direct imaging of the vortex unlikely. Instead, we propose an experiment to indirectly probe the vortex density of states with laser fields, in a scheme analogous to Scanning Tunneling Microscopy. Furthermore, it is shown that the vortex state causes a shift of the superfluid transition temperature, which can be understood as a finite size effect.

•Nov 25, 2003•0 citations

Vortex state in a superfluid Fermi gas near a Feshbach resonance

Yuki Kawaguchi, Tetsuo Ohmi

We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.

arXiv:cond-mat/0411018•Nov 1, 2004•0 citations

Vortex Arrays in a Rotating Superfluid Fermi Gas

David L. Feder

The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.

arXiv:cond-mat/0410097•Physical Review Letters•Nov 12, 2004•18 citations

Temperature dependence of a vortex in a superfluid Fermi gas

Stefano Simonucci, P. Pieri, Giancarlo Calvanese Strinati

The temperature dependence of an isolated quantum vortex, embedded in an otherwise homogeneous fermionic superfluid of infinite extent, is determined via the Bogoliubov--de Gennes (BdG) equations across the BCS-BEC crossover. Emphasis is given to the BCS side of this crossover, where it is physically relevant to extend this study up to the critical temperature for the loss of the superfluid phase, such that the size of the vortex increases without bound. To this end, two techniques are introduced. The first one solves the BdG equations with ``free boundary conditions,'' which allows one to determine with high accuracy how the vortex profile matches its asymptotic value at a large distance from the center, thus avoiding a common practice of constraining the vortex in a cylinder with infinite walls. The second one improves on the regularization procedure of the self-consistent gap equation when the interparticle interaction is of the contact type, and permits us to considerably reduce the time needed for its numerical integration by drawing elements from the derivation of the Gross-Pitaevskii equation for composite bosons starting from the BdG equations.

arXiv:1303.5229•Physical Review B•Jun 10, 2013•30 citations

Characteristic length scale and energy of a vortex line in a dilute, superfluid Fermi gas

Ø. Elgarøy

We calculate the characteristic length scale of a vortex line in a dilute, superfluid gas of fermionic atoms, and find that it is in general smaller, and has a weaker density dependence than the BCS coherence length. Taking this into account, we find the energy of a vortex line to be larger than has previously been estimated. As a consequence, the critical frequency for formation of vortices in trapped fermion gases can be significantly larger than earlier calculations have suggested.

arXiv:cond-mat/0111440•Nov 22, 2001•0 citations
The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.
The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov--de Gennes theory. Various thermodynamic properties are calculated, and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied, and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.
Dilute atomic gases have become a powerful tool for studying many-body quantum mechanics. The best example of this is the achievement of Bose-Einstein condensation in 1995 in a gas of Bose atoms, a discovery which has invoked a confluence of ideas from condensed matter, atomic and nuclear physics. Now a concerted research effort is focused on creating and studying a BCS superfluid in an atomic Fermi gas. In the work presented here we study in detail pairing superfluidity in a Fermi gas of atoms, by self-consistently solving the Bogoliubov-de Gennes equations, both for bulk systems, and for atoms in a harmonic confining potential. A critical part of this work is the derivation of a regularized theory, which is formulated entirely in terms of physically measurable quantities, such that a quantitative comparison between theory and experiment is possible with no adjustable parameters. The resulting equations form a non-linear problem, and the accurate numerical solution of this poses a formidable challenge. A major component of this thesis is the development of efficient computational approaches to overcome these difficulties. Based on the linear response of the gas to a twisting of the order parameter phase, the superfluid density can be defined as a generalized elasticity of the system. Using finite temperature perturbation theory we calculate the superfluid density in an inhomogeneous system. We investigate the structure and thermodynamic properties of a singly quantized vortex line in a gas of superfluid fermionic atoms, making the first quantitative determination the critical rotation frequency for thermodynamic stability of the vortex state, and study the nature of the bound states in the vortex core. These excitations fill the core, making direct imaging of the vortex unlikely. Instead, we propose an experiment to indirectly probe the vortex density of states with laser fields, in a scheme analogous to Scanning Tunneling Microscopy. Furthermore, it is shown that the vortex state causes a shift of the superfluid transition temperature, which can be understood as a finite size effect.
We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.
The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.
The temperature dependence of an isolated quantum vortex, embedded in an otherwise homogeneous fermionic superfluid of infinite extent, is determined via the Bogoliubov--de Gennes (BdG) equations across the BCS-BEC crossover. Emphasis is given to the BCS side of this crossover, where it is physically relevant to extend this study up to the critical temperature for the loss of the superfluid phase, such that the size of the vortex increases without bound. To this end, two techniques are introduced. The first one solves the BdG equations with ``free boundary conditions,'' which allows one to determine with high accuracy how the vortex profile matches its asymptotic value at a large distance from the center, thus avoiding a common practice of constraining the vortex in a cylinder with infinite walls. The second one improves on the regularization procedure of the self-consistent gap equation when the interparticle interaction is of the contact type, and permits us to considerably reduce the time needed for its numerical integration by drawing elements from the derivation of the Gross-Pitaevskii equation for composite bosons starting from the BdG equations.