Josephson effect and quantum merging of two Bose superfluids

We consider the Josephson effect when two independent Bose superfluids are weakly connected. In the presence of interparticle interaction and based on the calculations of the one-particle density matrix of the whole system, we find that the one-particle density matrix can be factorized which satisfies the general criterion of Bose superfluid proposed by Penrose and Onsager. By introducing an effective order parameter for the whole system, our researches show that there is Josephson effect for two independent Bose superfluids.