Decay of a Quantum Knot

Abstract

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...

Knot Morphing Algorithm for Quantum `Fragile Topology'

“…The concept of knotted electromagnetic fields led to the first experimental images of topological three-dimensional skyrmions [13]. The timing of knot creation [20] and decay [19] are central to modeling quantum properties, as further explored here. Recent analysis of quantum manifolds [11] shares fundamental ideas with the surfaces presented here.…”

Vortex patterns of atomic Bose-Einstein condensates in a density-dependent gauge potential

“…Dimensionality plays a central role in the physics of vortices -for two-dimensional quantum fluids experiments have demonstrated different topological phase transitions, prominent examples being the quantum spin Hall effect and the Berezinskii Kosterlitz Thouless transition, both of which have been realized with ultracold atoms [4,5]. In the three-dimensional context, more elaborate topological configurations are available, such as knots [6][7][8], skyrmions [9,10] and the related problem of engineering analogies of the magnetic monopole [11,12].…”

Spin-orbit coupled spin-1 Bose-Einstein condensate flow past an obstacle in the presence of a Zeeman field

“…Dynamical properties also play an important role in characterizing spinor BECs. In the past decade, various topological collective excitations including exotic vortex or vortex pair [36][37][38][39][40][41][42][43], soliton [44][45][46][47][48][49][50], knot [51][52][53], skyrmion [54][55][56][57][58][59] have been proposed and their dynamical stability have either been theoretically discussed or experimentally verified in the framework of spinor BECs. Recently, a variety of studies were performed on the dynamics of a scalar BEC flow past an obstacle, especially after the experimental observation of the induced vortex-antivortex pairs [60,61], which have been shown to exhibit extraordinary behaviors [62][63][64][65][66][67][68][69][70].…”