where ψ ψ 0 is the value of the condensate wavefunction at ∞ ∞ , and ξ ξ = ℏ ℏ / 2 m n 0 g = 1 / 8 π π a s n 0 is the coherence length (a.k.a. the healing length, see below). This solution represents the dark soliton, since there is a deficit of condensate in a space of nonzero density. The dark soliton is also a type of topological defect, since ψ ψ flips between positive and negative values across the origin, corresponding to a π π phase shift.