Non-Abelian Josephson effect in spinor Bose-Einstein condensates

We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which incorporates the non-Abelian Josephson effect and has very different density and spin tunneling characteristics compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.