Tying quantum knots

Abstract

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].

Helicity, topology, and Kelvin waves in reconnecting quantum knots

“…The recent experimental creation of quantum knots in the laboratory [21] shows also a promising application for the quantification and evolution of the topological complexity of quantum vortices.…”

“…However, numerical studies of Burgers-type vortices indicate that helicity is not conserved [20]. While experiments studying helicity in quantum flows have not been done yet, the recent experimental creation of quantum knots in a Bose-Einstein condensate in the laboratory [21] is a significant step in that direction.…”

“…The GPE models superfluids and Bose-Einstein condensates (BECs) (for which the creation of quantum knots has been recently demonstrated in the laboratory [21]) near zero temperature. We present a fluid-like regularized definition for the helicity, which solves the problem arising from the singularities in the velocity and the vorticity produced by the topological defects of the quantum flow, and links quantum knots with helicity as measured in fluid dynamics.…”

Models of random knots

“…C. In current research, such knotting phenomena are theoretically analyzed, numerically simulated, and experimentally created or identified in various physical systems. To mention some examples: knotted vortices in classical fluid flow (Kleckner and Irvine 2013) and in superfluids (Hall et al 2016;Kleckner et al 2016), optical vortices in laser beams (Dennis et al 2010), magnetic fields in plasma (Berger 1999), superposition of states in quantum mechanics (Berry 2001), and also nonlinear waves in biological and chemical excitable media (Winfree and Strogatz 1984).…”

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

“…Recent efforts in spin-1 BECs have led to the in situ observation of a singly quantized vortex splitting into a pair of HQVs [9], confirming theoretical prediction [8], and to controlled preparation of coreless-vortex textures [26][27][28], the analogs of Dirac [22] and 't Hooft-Polyakov [29] monopoles, and particlelike solitons [30]. Our results for spin-2 reveal a defect-structure phenomenology considerably richer than that in the spin-1 BECs [8,[31][32][33][34].…”