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Topological defects play important roles throughout nature, appearing in contexts as diverse as cosmology, particle physics, superfluidity, liquid crystals, and metallurgy. Point defects can arise naturally as magnetic monopoles resulting from symmetry breaking in grand unified theories. We devised an experiment to create and detect quantum mechanical analogs of such monopoles in a spin-1 Bose-Einstein condensate. The defects, which were stable on the time scale of our experiments, were identified from spin-resolved images of the condensate density profile that exhibit a characteristic dependence on the choice of quantization axis. Our observations lay the foundation for experimental studies of the dynamics and stability of topological point defects in quantum systems.

We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.

As topologically stable objects in field theories, knots have been put forward to explain various persistent phenomena in systems ranging from atoms and molecules to cosmic textures in the universe. Recent experiments have reported the observation of knots in different classical contexts. However, no experimental observation of knots has yet been reported in quantum matter. Here we demonstrate the experimental creation and detection of knot solitons in the order parameter of a spinor Bose–Einstein condensate. The observed texture corresponds to a topologically nontrivial element of the third homotopy group and exhibits the celebrated Hopf fibration, which unites many seemingly unrelated physical phenomena. Our work calls for future studies of the stability and dynamics knot solitons in the quantum regime. Knots have been observed in a variety of classical systems, but so far not in the quantum regime. Knot solitons have now been created in a spinor Bose–Einstein condensate, exhibiting interesting topological structures, including Hopf fibration.

Topological defects play important roles throughout nature, appearing in contexts as diverse as cosmology, particle physics, superfluidity, liquid crystals, and metallurgy. Point defects can arise naturally as magnetic monopoles resulting from symmetry breaking in grand unified theories. We devised an experiment to create and detect quantum mechanical analogs of such monopoles in a spin-1 Bose-Einstein condensate. The defects, which were stable on the time scale of our experiments, were identified from spin-resolved images of the condensate density profile that exhibit a characteristic dependence on the choice of quantization axis. Our observations lay the foundation for experimental studies of the dynamics and stability of topological point defects in quantum systems.

We introduce topologically stable three-dimensional skyrmions in the cyclic and biaxial nematic phases of a spin-2 Bose-Einstein condensate. These skyrmions exhibit exceptionally high mapping degrees resulting from the versatile symmetries of the corresponding order parameters. We show how these structures can be created in existing experimental setups and study their temporal evolution and lifetime by numerically solving the three-dimensional Gross-Pitaevskii equations for realistic parameter values. Although the biaxial nematic and cyclic phases are observed to be unstable against transition towards the ferromagnetic phase, their lifetimes are long enough for the skyrmions to be imprinted and detected experimentally.

We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.

We study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field.