Vortex-antivortex labyrinth wavefunction

We discuss a possibility of a pinning of quantized matter wave vortices by optical vortices in specially arranged optical dipole traps. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum to support ldquoantiferromagnet-likerdquo matter waves. The separable Hamiltonian for matter waves is proposed which allows to factorize of the 3D -wavefunction exactly in a product of 1D - harmonic oscillatorpsilas ground state and 2D - vortex-antivortex wavefunction. The wavefunctionpsilas phase gradient field associated with the field of classical velocities via Madelung transformation forms labyrinth-like structure. The macroscopic wavefunction of periodically spaced BEC superfluid vortices appears to be less influenced by decoherence.