Interaction-induced interference for two independent Bose-Einstein   condensates
  After removing the double-well potential trapping two initially independent Bose condensates, the density expectation value is calculated when both the exchange symmetry of identical bosons and interatomic interaction are considered. The density expectation value and evolution equations are obtained based on both the first-quantization and second-quantization methods. When the interatomic interaction is considered carefully, after the overlapping of two initially independent condensates, it is shown that there is a nonzero interference term in the density expectation value. It is found that the calculated density expectation value with this model agrees with the interference pattern observed in the experiment by Andrews (Science 275, 637 (1997)). The nonzero interference term in the density expectation value physically arises from the exchange symmetry of identical bosons and interatomic interaction which make two initially independent condensates become coherent after the overlapping. For two initially independent condensates, our researches show that there is an interaction-induced coherence process. 
Hongwei Xiong, Shujuan Liu, Mingsheng Zhan