Numerical study of entangled helical spin currents in a spinor Bose-Einstein condensate

We numerically study the dynamics of perfectly helical spin currents where two counter-propagating spin currents are quantum-mechanically entangled. A spin-1 condensate is initially prepared at the m = 0 magnetic sublevel in a one-dimensional torus. The atoms are assumed to interact via the s-wave scattering channel which parametrically generates an entangled pair of m = 1 and -1 atoms from two m = 0 atoms. The pair of m = 1 and -1 atoms acquire oppositely directed momenta via the Bragg diffraction, while they maintain the quantum-mechanical spin correlations. As a result, a nonzero spin current flows in the torus with no net mass current.