Superfluid vortices · quantized circulation · Feynman's rule
In a Bose-Einstein condensate described by a macroscopic wavefunction ψ = √n·e^(iφ), the superfluid velocity v = (ℏ/m)∇φ is irrotational everywhere except at vortex cores where ψ=0. Feynman's rule (1955) states that upon rotation at angular velocity Ω, vortices form with areal density n_v = 2mΩ/h, so that on average the condensate mimics solid-body rotation. Each vortex carries exactly one quantum of circulation κ = h/m. The vortices arrange into an Abrikosov-like triangular Feynman lattice (Tkachenko lattice), whose normal modes (Tkachenko waves) have been observed in ⁸⁷Rb and ²³Na BECs.