Topologically protected pure helicity cascade in non-Abelian quantum turbulence

Abstract

By numerically studying non-Abelian quantum turbulence, we find that the helicity cascade and the inverse energy cascade are topologically protected against reconnection of vortices and lead to the energy spectrum $E(k) \propto k^{-7/3}$ for a large-scale energy injection and $E(k) \propto k^{-5/3}$ for a small-scale energy injection with a large-scale web of non-Abelian vortices. Our prediction can be tested in the cyclic phase of a spin-2 spinor Bose-Einstein condensate.