Magnetic monopoles — particles carrying a single magnetic charge — have never been seen. Analogues of these entities have now been produced in an ultracold cloud of rubidium atoms. See Letter p.657
If you have ever broken a magnet in two, you will know that each of the new pieces has a 'north' and a 'south' pole — just like the original. Despite being allowed in theory, a north pole separated from its south to create an isolated magnetic monopole has not been found. On page 657 of this issue, Ray et al.1 report how they have created a 'Dirac monopole' by engineering an environment that mimics a monopole's magnetic field in a cloud of rubidium atoms. Using direct imaging, the authors observe a distinct signature of the Dirac monopole in this quantum system: a line of zero atomic density that pierces the cloud and terminates at the monopole. This 'Dirac string' is a defect that allows the system's quantum-mechanical phase to satisfy constraints imposed by the monopole's characteristic geometry and the wave-like nature of matter.
The duality of electric and magnetic fields in classical electromagnetism makes it especially surprising that no magnetic monopole has been found to complement the electric charge. In his 1931 paper2, Paul Dirac showed that the theory of quantum mechanics, like its classical counterpart, allows the existence of monopoles. Furthermore, he demonstrated that if even a single monopole exists, electrical charge must come in discrete packets, which provides a possible explanation for the well-established observation that electrical charge is quantized. Although experiments have failed to find definitive evidence for the magnetic monopole3, researchers continue to seek this elusive particle with ever more powerful tools (see, for example, refs 4,5,6).
To explore the quantum properties of matter near a monopole, Ray and colleagues used a Bose–Einstein condensate (BEC) of ultracold rubidium atoms. A BEC is a collection of quantum particles in which the wave-like nature of matter dominates and the ensemble behaves as a single wave. Although the wave's phase — the quantity that determines the local amplitude of the wave as it oscillates between its minimum and maximum values — is always evolving, phase relationships between different spatial points in a BEC are rigidly maintained and give the condensate well-defined long-range quantum correlations.
Magnetic fields exert a force, called the Lorentz force, on charged particles in a direction that is perpendicular to both that of the particle's velocity and the magnetic field. In quantum mechanics, the velocity at a specific point is proportional to the spatial variation in phase, and magnetic fields modify this variation to ensure that the Lorentz force is realized. Because a monopole's magnetic-field lines emerge radially from the source, its field geometry is fundamentally different from that of a conventional magnet, whose field lines have no end points (Fig. 1a, b). This geometric difference is reflected in distinct spatial phase relationships associated with each magnetic-field source.
The phase difference between two spatial points can be visualized by relating it to the change in velocity, owing to the Lorentz force, of a classical particle travelling along a trajectory between the points. For conventional magnetic fields, the change in velocity between start and finish is independent of the particle's path (Fig. 1c). By contrast, the monopole's geometry results in a path-dependent final velocity (Fig. 1d), which suggests that, because of the relationship between velocity and phase variation, the final phase of a quantum particle depends on its trajectory. In quantum mechanics, however, all paths are sampled in a journey from one point to another. Because the phase can have only a single value at each point in space, the system must account for all possibilities. One solution to this ambiguity is the emergence of an infinitely thin filament extending from the monopole, along which the phase is singular (undefined) and there is zero probability that any atom resides there. Rapid phase variations wrap around this Dirac string (see Fig. 1 of the paper1) and result in large, swirling velocities, which are physically manifested in a BEC as a vortex. This motion corresponds to the classical particles' acquisition of large velocities circling around the final point in the visualization described above.
In their study, Ray et al. produce a synthetic magnetic field in a BEC whose phase variations accompany spatial variations in intrinsic angular momentum (spin) of the BEC's atoms. Previous methods implemented synthetic fields using rotating BECs7 or light-assisted atomic transitions8. To create a Dirac monopole, which is the magnetic monopole's generalization in a quantum system, the authors engineered an environment in which the preferred spin varies in space, and tailored these variations using an impressively stable and precise apparatus. With these techniques, they identified a zero-density Dirac string that terminated within the BEC at the Dirac monopole. They also observed that the phase variation around the Dirac string is consistent with predictions, and showed that the spatial distribution of the atoms' spin matches numerical calculations.
This creation of a Dirac monopole in a BEC is a beautiful demonstration of quantum simulation9, a growing research field that uses real quantum systems to model others that are difficult to make, calculate or observe. Ray et al. have shown that experimental atomic-physics techniques can provide tangible systems in which to explore phenomena across disciplines. Although this technique is limited in its geometry, the authors' synthetic-magnetic-field method is free from the atomic-number losses caused by light-assisted heating that plague other techniques8. Their experiments will lead to further exploration of the dynamics and excitations of a Dirac monopole, and provide the promise of producing large effective magnetic fields by means of 'vortex pumping'10, which may in turn yield analogues of quantum Hall states11 and other exotic quantum configurations.
Although these results offer only an analogy to a magnetic monopole, their compatibility with theory reinforces the expectation that this particle will be detected experimentally. As Dirac said2 in 1931, referring to the magnetic monopole: “under these circumstances one would be surprised if Nature had made no use of it.”
Ray, M. W., Ruokokoski, E., Kandel, S., Möttönen, M. & Hall, D. S. Nature 505, 657–660 (2014).
Dirac, P. A. M. Proc. R. Soc. Lond. A 133, 60–72 (1931).
Milton, K. A. Rep. Prog. Phys. 69, 1637–1711 (2006).
Pinfold, J. L. Radiat. Measure. 44, 834–839 (2009).
Adrián-Martínez, S. et al. Astropart. Phys. 35, 634–640 (2012).
Abbasi, R. et al. Phys. Rev. D 87, 022001 (2013).
Fetter, A. L. Rev. Mod. Phys. 81, 647–691 (2009).
Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Rev. Mod. Phys. 83, 1523–1543 (2011).
Bloch, I., Dalibard, J. & Nascimbène, S. Nature Phys. 8, 267–276 (2012).
Möttönen, M., Pietilä, V. & Virtanen, S. M. M. Phys. Rev. Lett. 99, 250406 (2007).
Roncaglia, M., Rizzi, M. & Dalibard, J. Sci. Rep. 1, 43 (2011).