Observation of Dirac monopoles in a synthetic magnetic field

Abstract

Magnetic monopoles—particles that behave as isolated north or south magnetic poles—have been the subject of speculation since the first detailed observations of magnetism several hundred years ago1. Numerous theoretical investigations and hitherto unsuccessful experimental searches2 have followed Dirac’s 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field3. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge3,4. Although analogues of magnetic monopoles have been found in exotic spin ices5,6 and other systems7,8,9, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10, 11, 12, 13). Here we demonstrate the controlled creation14 of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose–Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum mechanical entities in a controlled environment.

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Figure 1: Schematic representations of the monopole creation process and experimental apparatus.
Figure 2: Experimental creation of Dirac monopoles.
Figure 3: Comparison between experiment and simulation.
Figure 4: Quantitative comparison between experiment and simulation.

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Acknowledgements

We acknowledge funding by the National Science Foundation (grants PHY–0855475 and PHY–1205822), by the Academy of Finland through its Centres of Excellence Program (grant no. 251748) and grants (nos 135794, 272806 and 141015), and the Finnish Doctoral Programme in Computational Sciences. CSC – IT Center for Science Ltd is acknowledged for computational resources (project no. ay2090). We thank G. Volovik, M. Krusius, R. H. Romer, M. Nakahara and J. R. Friedman for their comments on the manuscript. We also thank H. Valja for his artistic input. M.W.R. and D.S.H. acknowledge discussions with R. P. Anderson and K. Jagannathan, and experimental assistance from N. B. Bern.

Author information

M.W.R., S.K. and D.S.H. developed and conducted the experiments, after which M.W.R. and D.S.H. analysed the data. E.R. performed the numerical simulations under the guidance of M.M., who also developed the gauge transformations presented in Supplementary Information. Interactive feedback between the experiments and simulations carried out by M.W.R., D.S.H., E.R. and M.M. was essential to achieving the reported results. All authors discussed both experimental and theoretical results and commented on the manuscript.

Correspondence to D. S. Hall.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Decay of the doubly quantized vortex.

Images of the condensate time evolution after moving the magnetic field zero completely through the condensate. The evolution time is shown at the bottom right of each panel. The maximum pixel intensity corresponds to a peak column density , and the field of view is 246 μm × 246 μm. Each image represents a separate condensate, and . After roughly 10 ms the vortex splits in two, demonstrating the initial 4π phase winding of the nodal line.

Extended Data Figure 2 Additional representative images of Dirac monopoles.

Each row contains images of the same condensate. The maximum pixel intensity corresponds to , and the field of view is 220 μm × 220 μm in the vertical images and 285 μm × 285 μm in the horizontal images. The arrow points to the density depletion that is identified as the nodal line. In ac, we use the same protocol outlined in the paper: an off-centre monopole (a); an angled nodal line that is visible in the side image but not in the vertically directed image (b); and a nodal line that appears to be splitting into two vortices in the |m = −1〉 component (c). d, An example of a monopole spin structure in which the creation ramp is as described in the text but the projection ramp is reversed (that is, Bz is rapidly increased until ). e, Monopole spin structure created by moving the field zero into the condensate from below with . The projection ramp is performed as described in d.

Extended Data Figure 3 Numerical simulation of integrated particle densities before expansion.

Vertically (a) and horizontally (b) integrated particle densities of a condensate just before the projection ramp, with Bz,f chosen such that the monopole is in the centre of the condensate. The fields of view are 17.2 μm × 17.2 μm (a) and 17.2 μm × 11.4 μm (b); in b, it is reduced in the z direction for a more convenient comparison with the simulations shown in Fig. 3. The maximum pixel intensity corresponds to .

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Supplementary Information

This file contains Supplementary Text and Supplementary Figure 1 providing additional information regarding the underlying theory of the system. (PDF 135 kb)

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Ray, M., Ruokokoski, E., Kandel, S. et al. Observation of Dirac monopoles in a synthetic magnetic field. Nature 505, 657–660 (2014) doi:10.1038/nature12954

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