Temperature dependence of a vortex in a superfluid Fermi gas

TL;DR

This study investigates how a quantum vortex in a fermionic superfluid changes with temperature across the BCS-BEC crossover, introducing new numerical techniques for high-accuracy solutions near the critical temperature.

Contribution

It presents two novel computational methods for solving the Bogoliubov-de Gennes equations, improving accuracy and efficiency in studying vortex profiles at finite temperatures.

Findings

Vortex size diverges near the critical temperature on the BCS side.

New boundary condition technique improves vortex profile matching.

Enhanced regularization reduces computational time significantly.

Abstract

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 novel 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 inter-particle interaction is of the contact type, and permits 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.