Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity

Area of Science:

• Nonlinear physics
• Topological solitons
• Quantum gases

Background:

• Toroidal modes, or Hopfions, with twist (s) and vorticity (m) are observed in diverse fields.
• Typically require multicomponent systems or toroidal potentials for generation.

Purpose of the Study:

• To demonstrate the creation of stable Hopfion solitons in a single-component system without linear potentials.
• To explore the stability and properties of these toroidal modes.

Main Methods:

• Utilizing a single-component nonlinear system with radially dependent repulsive nonlinearity.
• Investigating steep and smooth modulation profiles.
• Deriving an approximate analytical solution for specific configurations (s=1, m=0).

Main Results:

• Stable toroidal Hopfion solitons with s=1 and m=0, 1, 2 were successfully created.
• Stability was confirmed for m≤1; Hopfions with s>1 were not found.
• An analytical solution for the s=1, m=0 twisted ring was obtained, showing solid-ring rotation under torque.

Conclusions:

• Stable, single-component Hopfion solitons can be generated via tailored nonlinearity.
• These solitons exhibit controllable dynamics, such as rotation under external torque.
• Potential implementation in Bose-Einstein condensates using Feshbach resonance and magnetic fields.