Quantum fluctuations of a vortex in a dilute Bose-Einstein condensate

TL;DR

This paper investigates quantum fluctuations of a vortex in a dilute Bose-Einstein condensate, revealing that actual vortex position fluctuations are much smaller than simple models suggest, using a number-conserving Bogoliubov approach.

Contribution

It demonstrates that vortex position fluctuations are negligible when analyzed with a number-conserving Bogoliubov theory, challenging previous simple estimates.

Findings

Vortex position fluctuations are minimal compared to simple Gaussian estimates.

The Bogoliubov mode does not contribute to vortex position fluctuations.

Phonons contribute to fluctuations but are significantly smaller than naive predictions.

Abstract

A vortex in a quasi two-dimensional Bose-Einstein condensate is subject to the Magnus force and can be effectively described as a planar particle in a uniform magnetic field. Quantization of this effective particle leads to the lowest Landau level where the most localized wave function is a gaussian. In this gaussian state vortex position seems to fluctuate with an average magnitude set by the magnetic width of the gaussian. We readdress this problem using the number-conserving version of the Bogoliubov theory. We find that the Bogoliubov mode that might be interpreted as a fluctuation of vortex position actually does not contribute to position fluctuation at all. The only non-zero contribution comes from phonons but it is an order of magnitude less than the simple estimate, based on the magnetic width of the effective gaussian wave packet.