Density dip and phase kink propagating in a Bose-Einstein condensate
Soliton velocity v0.30
Interaction g2.0
Healing length ξ3.0
Add 2nd soliton-0.30
The Gross-Pitaevskii equation iℏ∂ψ/∂t = (−ℏ²/2m ∂²/∂x² + g|ψ|²)ψ governs a Bose-Einstein condensate.
A dark soliton is an exact solution: ψ(x,t) = n₀[iv/c + √(1−v²/c²) tanh((x−vt)/(√2 ξ √(1−v²/c²)))],
where ξ = ℏ/√(2mgn₀) is the healing length, c = √(gn₀/m) is the sound speed.
The density shows a dip (dark region) and the phase shows a kink of 2arccos(v/c).
Dark solitons pass through each other with a phase shift upon collision.