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

Jacek Dziarmaga·Jakub Meisner
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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.

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Jacek Dziarmaga, Jakub Meisner. 2004-10-27. Quantum fluctuations of a vortex in a dilute Bose-Einstein condensate. https://doi.org/10.1088/0953-4075%2F38%2F23%2F004

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