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## "Quantum phases of vortices in rotating Bose-Einstein condensates", Nigel Cooper, Nicola Wilkin, Mike Gunn, 2001

*Reviewed February 3, 2024*

*Citation:* Cooper, Nigel R., Nicola K. Wilkin, and J. M. F. Gunn. "Quantum phases of vortices in rotating Bose-Einstein condensates." Physical review letters 87.12 (2001): 120405.

*Web:* https://arxiv.org/abs/cond-mat/0107005

*Tags:* Physical, Hardware, Majorana-fermions, Quantum-hall-effect

This article is one of the first in a series which
established a new way in which (possibly non-abelian) topological phases
could appear in the wild: rapidly rotating Bose-Einstein condensates.
The idea is that the integral rotational invariance you get from the quantum Hall effect
could also appear from a more external rotation. Like, for instance, literally spinning your system around in a circle.
There is a "filling fraction" quantity you can define, which depends on the angular momentum of your rotation,
which determines the physics of the system. Follow up work found that the wave functions
often looked like the non-abelian Read-Rezayi wavefunctions:

> Cooper, N. R. "Exact ground states of rotating Bose gases close to a Feshbach resonance." Physical review letters 92.22 (2004): 220405.

> Rezayi, E. H., N. Read, and N. R. Cooper. "Incompressible liquid state of rapidly rotating bosons at filling factor 3/2." Physical review letters 95.16 (2005): 160404.

> Schweikhard, Volker, et al. "Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level." Physical review letters 92.4 (2004): 040404.

This approach never seems to have got mainstream appeal. People
stopped publishing papers. The most modern review is a Airlia Shaffer's PhD thesis:

> Shaffer, Airlia. Bosonic Quantum Hall States from Rapidly Rotating Bose-Einstein Condensates. Diss. Massachusetts Institute of Technology, 2023.