Non-Abelian Josephson effect between two spinor Bose-Einstein condensates in double optical traps

We investigate the non-Abelian Josephson effect in spinor Bose-Einstein condensates with double optical traps. We propose, for the first time, a real physical system which contains non-Abelian Josephson effects. The collective modes of this weak coupling system have very different density and spin tunneling characters comparing to the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps respectively, which are a crucial feature of the non-Abelian Josephson effects. We also give an experimental protocol to observe this novel effect in future experiments.