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We provide a simple physical picture of the loss of coherence between twocoherently split one-dimensional Bose-Einstein condensates. The source of thedephasing is identified with nonlinear corrections to the elementary excitationenergies in either of the two independent condensates. We retrieve the resultby Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on thesubexponential decay of the cocherence for the large time, however, the scalingof the characteristic decoherence time differs.

Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence