We demonstrate that the winding number of a toroidal Bose-Einstein condensate can be deterministically and robustly engineered by manipulating the motion of dark solitons via nonlinear coupling with the localized waves driven by external forces. As the soliton velocity relative to the background crosses zero, the emergence of a density zero, inducing the phase singularity, leads to a quantized jump in the winding number whose direction is determined by the direction of the velocity crossing. This approach enables the programmable manipulation of the winding number, and allows for versatile tailoring by accelerating multiple dark solitons. Our results are supported by full three-dimensional numerical simulations, while the experimental feasibility is discussed using state-of-the-art techniques. The explicit relation between the winding number and the persistent current in the ring geometry facilitates the design of compact rotation sensors, and opens new avenues for developing topological physics and advancing quantum technologies.

Close

PrevNext

View figure in article

• Cold atoms & matter waves
• Bose-Einstein condensates
• Solitons