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/0111440

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

Ø. Elgarøy

Published Nov 22, 2001• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/0111440

Related papers

Vortex state in superfluid trapped Fermi gases at zero temperature

Georg M. Bruun, Luciano Viverit

We discuss various aspects of the single vortex state of a dilute superfluid atomic Fermi gas at $T=0.$ The energy of the vortex in a trapped gas is calculated and we provide an expression for the thermodynamic critical rotation frequency of the trap for its formation. Furthermore, we propose a method to detect the presence of a vortex by calculating the effect of its associated velocity field on the collective mode spectrum of the gas.

arXiv:cond-mat/0106011•Physical Review A•Nov 14, 2001•25 citations

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

Nicolai Gayle Nygaard, Georg M. Bruun, Charles W. Clark +1 more

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.

arXiv:cond-mat/0210526•Physical Review Letters•May 30, 2003•50 citations

Vortex mass in superfluid Fermi gases along the BEC-BCS crossover

Lucas Levrouw, Hiromitsu Takeuchi, Jacques Tempere

Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving toward the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.

arXiv:2505.12590•Physical Review A•Sep 17, 2025•1 citation

Vortices in Trapped Superfluid Fermi Gases

Mirta Rodríguez, Gheorghe Sorin Paraoanu, Päivi Törmä

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

arXiv:cond-mat/0104491•Physical Review Letters•Aug 20, 2001•19 citations

Tkachenko modes in a superfluid Fermi gas at unitarity

Gentaro Watanabe A, Marco Cozzini, S. Stringari

We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elastohydrodynamic theory and properly account for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.

arXiv:0709.2757•Physical Review A•Feb 7, 2008•3 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
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.
We discuss various aspects of the single vortex state of a dilute superfluid atomic Fermi gas at T=0.T=0.T=0. The energy of the vortex in a trapped gas is calculated and we provide an expression for the thermodynamic critical rotation frequency of the trap for its formation. Furthermore, we propose a method to detect the presence of a vortex by calculating the effect of its associated velocity field on the collective mode spectrum of the gas.
Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving toward the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.
We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.
We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elastohydrodynamic theory and properly account for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.
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.