Bose-Einstein condensates with a bent vortex in rotating traps

TL;DR

This paper investigates the shape and stability of vortex lines in rotating Bose-Einstein condensates, combining numerical simulations and analytical models to understand vortex bending and thermal fluctuation effects.

Contribution

It introduces an analytical energy functional for bent vortex lines in cigar-shaped condensates, explaining their bending and predicting critical rotation frequencies.

Findings

Vortex lines are bent in cigar-shaped traps, consistent with previous predictions.

The analytical model accurately predicts the minimal rotation frequency for vortex stabilization.

Thermal fluctuations can be analyzed using Monte Carlo sampling within the Bogoliubov approximation.

Abstract

We consider a 3D dilute Bose-Einstein condensate at thermal equilibrium in a rotating harmonic trap. The condensate wavefunction is a local minimum of the Gross-Pitaevskii energy functional and we determine it numerically with the very efficient conjugate gradient method. For single vortex configurations in a cigar-shaped harmonic trap we find that the vortex line is bent, in agreement with the numerical prediction of Garcia-Ripoll and Perez-Garcia, Phys.Rev.A 63, 041603 (2001). We derive a simple energy functional for the vortex line in a cigar-shaped condensate which allows to understand physically why the vortex line bends and to predict analytically the minimal rotation frequency required to stabilize the bent vortex line. This analytical prediction is in excellent agreement with the numerical results. It also allows to find in a simple way a saddle point of the energy, where the vortex line is in a stationary configuration in the rotating frame but not a local minimum of energy. Finally we investigate numerically the effect of thermal fluctuations on the vortex line for a condensate with a straight vortex: we can predict what happens in a single realization of the experiment by a Monte Carlo sampling of an atomic field quasi-distribution function of the density operator of the gas at thermal equilibrium in the Bogoliubov approximation.