We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.

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Persistent topological defects and textures are particularly dramatic consequences of superfluidity. Among the most fascinating examples are the singular vortices arising from the rotational symmetry group SO(3), with surprising topological properties illustrated by Dirac’s famous belt trick. Despite considerable interest, controlled preparation and detailed study of vortex lines with complex internal structure in fully three-dimensional spinor systems remains an outstanding experimental challenge. Here, we propose and implement a reproducible and controllable method for creating and detecting a singular SO(3) line vortex from the decay of a non-singular spin texture in a ferromagnetic spin-1 Bose–Einstein condensate. Our experiment explicitly demonstrates the SO(3) character and the unique spinor properties of the defect. Although the vortex is singular, its core fills with atoms in the topologically distinct polar magnetic phase. The resulting stable, coherent topological interface has analogues in systems ranging from condensed matter to cosmology and string theory.

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 experimentally study the dynamics of quantum knots in a uniform magnetic field in spin-1 Bose-Einstein condensates. The knot is created in the polar magnetic phase, which rapidly undergoes a transition towards the ferromagnetic phase in the presence of the knot. The magnetic order becomes scrambled as the system evolves, and the knot disappears. Strikingly, over long evolution times, the knot decays into a polar-core spin vortex, which is a member of a class of singular SO(3) vortices. The polar-core spin vortex is stable with an observed lifetime comparable to that of the condensate itself. The structure is similar to that predicted to appear in the evolution of an isolated monopole defect, suggesting a possible universality in the observed topological transition.Topological defects and textures provide intriguing conceptual links between many otherwise distant branches of science [1,2]. They appear in various contexts ranging from condensed matter to high-energy physics and cosmology, and can be highly stable against weak perturbations. However, there can be mechanisms leading to the decay of the defects despite their topological stability. The decay can be induced by, for example, changes to the underlying symmetries or the finite size of the system [3].Spinor Bose-Einstein condensates (BECs) are one of the most fascinating systems available for the study of topological defects due to the diverse range of broken symmetries associated with the different magnetic phases of the system. In the scalar case, the spin degrees of freedom are inaccessible and the topology of the BEC is simply described by the broken U(1) symmetry, yielding one-dimensional solitons and vortex lines as the only possible topological defects of the system. Upon including the spin degrees of freedom, the internal symmetries of the gas become plentiful, allowing for a diverse set of excitations. For example, in spinor BECs there can be several types of vortices [4][5][6][7][8][9], skyrmions [10][11][12][13][14], monopoles [15][16][17][18][19], and quantum knots [20,21].Topologically stable knots are classified by a linking number (or Hopf charge) Q, which counts the number of times each preimage loop of the order parameter is linked with every other such loop [22]. In Ref. [21], the experimental creation of knots with Q = 1 was reported in the polar magnetic phase of spin-1 BECs. Alternative methods to create knots were theoretically proposed in Refs. [23,24]. During its evolution, the knot is predicted to facilitate the decay of the underlying polar magnetic phase into the ferromagnetic phase [20]. Prior to the present study, however, neither this nor any other prediction involving the temporal evolution of the knot has been experimentally tested beyond the preliminary investigations of Ref. [21]. * tuomas.ollikainen@aalto.fiIn this Letter, we report experimental observations of the evolution of the quantum knot in spin-1 87 Rb BECs in a uniform external magnetic field. We show that the knot structure begins to decay rapidly on a time sc...

Quantized vortices appear in physical systems from superfluids and superconductors to liquid crystals and high energy physics. Unlike their scalar cousins, superfluids with complex internal structure can exhibit rich dynamics of decay and even fractional vorticity. Here, we experimentally and theoretically explore the creation and time evolution of vortex lines in the polar magnetic phase of a trapped spin-1 87Rb Bose–Einstein condensate. A process of phase-imprinting a nonsingular vortex, its decay into a pair of singular spinor vortices, and a rapid exchange of magnetic phases creates a pair of three-dimensional, singular singly-quantized vortex lines with core regions that are filled with atoms in the ferromagnetic phase. Atomic interactions guide the subsequent vortex dynamics, leading to core structures that suggest the decay of the singly-quantized vortices into half-quantum vortices.

Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose–Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry.

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