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 ago 1 . Numerous theoretical investigations and hitherto unsuccessful experimental searches 2 have followed Dirac's 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field 3 . The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge 3,4 . Although analogues of magnetic monopoles have been found in exotic spin-ices 5,6 and other systems 7-9 , there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10-13).Here we demonstrate the controlled creation 14 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. * Present address: City of Hope, 1500 East Duarte Road, Duarte, California 91010, USA. 1 arXiv:1408.3133v1 [cond-mat.quant-gas] 13 Aug 2014Maxwell's equations refer neither to magnetic monopoles nor to the magnetic currents that arise from their motion. Although a simple symmetrisation with respect to the electric and magnetic fields, respectively E and B, leads to equations that involve these magnetic charges, it also seemingly prevents their description in terms of the familiar scalar and vector potentials, respectively V and A, alone. Because the quantum-mechanical Hamiltonian is expressed in terms of potentials, rather than electromagnetic fields, this modification immediately leads to serious theoretical challenges.In a celebrated paper that combined arguments from quantum mechanics and classical electrodynamics 3 , Dirac identified electromagnetic potentials consistent with the existence of magnetic monopoles. His derivation relies upon the observation that in quantum mechanics the potentials V and A influence charged particle dynamics either through the Hamiltonian or, equivalently, through modifications of the complex phase of the particle wavefunction.Armed with these equivalent perspectives, Dirac then considered the phase properties of a wavefunction pierced by a semi-infinite nodal line with nonzero phase winding. Physically, the vector potential, A * , and synthetic magnetic field, B * = ∇ × A * , are related to the superfluid velocity, v s , and vorticity, Ω = ∇ × v s , respectively. ...

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We study the dynamics of small vortex clusters with few (2-4) co-rotating vortices in Bose-Einstein condensates by means of experiments, numerical computations, and theoretical analysis. All of these approaches corroborate the counter-intuitive presence of a dynamical instability of symmetric vortex configurations. The instability arises as a pitchfork bifurcation at sufficiently large values of the angular momentum that induces the emergence and stabilization of asymmetric rotating vortex configurations. The latter are quantified in the theoretical model and observed in the experiments. The dynamics is explored both for the integrable two-vortex system, where a reduction of the phase space of the system provides valuable insight, as well as for the non-integrable three-(or more) vortex case, which additionally admits the possibility of chaotic trajectories.

Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science [1]. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent phenomena, from atoms and molecules [2] to ball lightning [3] and cosmic textures in the universe [4]. Recent experiments have observed knots in a variety of classical contexts, including nematic liquid crystals [5][6][7], DNA [8], optical beams [9, 10], and water [11]. However, no experimental observations of knots have yet been reported in quantum matter. We demonstrate here the controlled creation [12] and detection of knot solitons [13,14] in the order parameter of a spinor Bose-Einstein condensate. The experimentally obtained images of the superfluid directly reveal the circular shape of the soliton core and its accompanying linked rings. Importantly, the observed texture corresponds to a topologically non-trivial element of the third homotopy group [15] and demonstrates the celebrated Hopf fibration [16], which unites many seemingly unrelated physical contexts [17,18]. Our observations of the knot soliton establish an experimental foundation for future studies of their stability and dynamics within quantum systems [19].