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Spontaneous vortices in the formation of Bose–Einstein condensates

Abstract

Phase transitions are ubiquitous in nature, and can be arranged into universality classes such that systems having unrelated microscopic physics show identical scaling behaviour near the critical point. One prominent universal element of many continuous phase transitions is the spontaneous formation of topological defects during a quench through the critical point1,2,3. The microscopic dynamics of defect formation in such transitions are generally difficult to investigate, particularly for superfluids4,5,6,7. However, Bose–Einstein condensates (BECs) offer unique experimental and theoretical opportunities for probing these details. Here we present an experimental and theoretical study of the BEC phase transition of a trapped atomic gas, in which we observe and statistically characterize the spontaneous formation of vortices during condensation8,9. Using microscopic theories10,11,12,13,14,15,16,17 that incorporate atomic interactions and quantum and thermal fluctuations of a finite-temperature Bose gas, we simulate condensation and observe vortex formation in close quantitative agreement with our experimental results. Our studies provide further understanding of the development of coherence in superfluids, and may allow for direct investigation of universal phase transition dynamics.

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Figure 1: Schematic of spontaneous vortex formation.
Figure 2: Condensate formation and vorticity.
Figure 3: Vortices in the harmonic and toroidal traps.
Figure 4: BEC growth dynamics.

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Acknowledgements

We thank D. Roberts, B. Svistunov, E. Wright and W. Zurek for discussions. The experimental work was financially supported by the US National Science Foundation under grant no. 0354977, and by the Army Research Office. The theoretical work was financially supported by the Australian Research Council Centre of Excellence for Quantum-Atom Optics and the University of Queensland.

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Correspondence to Brian P. Anderson.

Supplementary information

Supplementary Information

This file contains a Supplementary Discussion, Supplementary Figures 1 and 2 with Legends, Supplementary Table 1, Supplementary Notes and Supplementary Video Legends 1-10 (PDF 369 kb)

Supplementary Video 1

Supplementary Video 1 shows a condensate formation in a harmonic trap with no resulting vortices. (MOV 2176 kb)

Supplementary Video 2

Supplementary Video 2 shows a condensate formation in a harmonic trap resulting in a single vortex that remains near trap centre. (MOV 2184 kb)

Supplementary Video 3

Supplementary Video 3 shows a condensate formation in a harmonic trap with three vortices at early times, two of which damp to leave one vortex at long times that is not vertically aligned. (MOV 2180 kb)

Supplementary Video 4

Supplementary Video 4 shows a condensate formation in a harmonic trap resulting in two oppositely charged vortices that precess about the centre in opposite directions. (MOV 2199 kb)

Supplementary Video 5

Supplementary Video 5 shows a condensate formation in a harmonic trap showing complicated vortex dynamics with flips of orientation and vortex reconnections. (MOV 2238 kb)

Supplementary Video 6

Supplementary Video 6 shows a condensate formation in a toroidal trap resulting in a single vortex that is trapped as a persistent current by the central barrier. (MOV 2213 kb)

Supplementary Video 7

Supplementary Video 7 shows a of condensate formation in a toroidal trap resulting in a persistent current with an additional vortex precessing about the central barrier (MOV 2215 kb)

Supplementary Video 8

Supplementary Video 8 shows of condensate formation in a toroidal trap with no resulting persistent current but a single vortex precessing about the centre. (MOV 2234 kb)

Supplementary Video 9

Supplementary Video 9 shows a of condensate formation in a toroidal trap with two vortices of the same charge, one of which is trapped on the central barrier. (MOV 2263 kb)

upplementary Video 10

Supplementary Video 10 shows a of condensate formation in a toroidal trap resulting in a doubly-charged persistent current. (MOV 2232 kb)

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Weiler, C., Neely, T., Scherer, D. et al. Spontaneous vortices in the formation of Bose–Einstein condensates. Nature 455, 948–951 (2008). https://doi.org/10.1038/nature07334

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