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arXiv:cond-mat/0312258 · Physical Review A

Vortex line in a neutral finite-temperature superfluid Fermi gas

Nicolai Gayle Nygaard, Georg M. Bruun, Barry I. Schneider, Charles W. Clark, D. Feder

Published May 20, 2004• 19 citations
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Abstract

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.

DOI
10.1103/physreva.69.053622

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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.
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.
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.
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.
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.
It has recently been shown that the spin-orbit coupling gives rise to topologically nontrivial and thermodynamically stable gapless superfluid phases when the pseudospin populations of an atomic Fermi gas are imbalanced, with the possibility of featuring Majorana zero-energy quasiparticles. In this paper, we consider a Rashba-type spin-orbit coupling, and use the Bogoliubov-de Gennes formalism to analyze a single vortex line along a finite cylinder with a periodic boundary condition. We show that the signatures for the appearance of core- and edge-bound states can be directly found in the density of single-particle states and particle-current density. In particular, we find that the pseudospin components counterflow near the edge of the cylinder, the strength of which increases with increasing spin-orbit coupling.