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We investigate the phase coherence of a trapped Bose-Einstein condensate thatundergoes a dynamical superfluid-insulator transition in the presence of aone-dimensional optical lattice. We study the evolution of the condensate aftera sudden displacement of the harmonic trapping potential by solving theGross-Pitaevskii equation, and comparing the results with the prediction of twoeffective 1D models. We show that, owing to the 3D nature of the system, thebreakdown of the superfluid current above a critical displacement is notassociated to a sharp transition, but there exists a range of displacements forwhich the condensate can recover a certain degree of coherence. We also discussthe implications on the interference pattern after the ballistic expansion asmeasured in recent experiments at LENS.Comment: 7 pages, 9 figure

Loss and revival of phase coherence in a Bose–Einstein condensate moving through an optical lattice