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We investigate the possibility that Bose-Einstein condensates (BECs), loadedon a 2D optical lattice, undergo - at finite temperature - aBerezinskii-Kosterlitz-Thouless (BKT) transition. We show that - in anexperimentally attainable range of parameters - a planar lattice of BECs isdescribed by the XY model at finite temperature. We demonstrate that theinterference pattern of the expanding condensates provides the experimentalsignature of the BKT transition by showing that, near the critical temperature,the k=0 component of the momentum distribution and the central peak of theatomic density profile sharply decrease. The finite-temperature transition fora 3D optical lattice is also discussed, and the analogies with superconductingJosephson junction networks are stressed through the text

Observable signature of the Berezinskii–Kosterlitz–Thouless transition in a planar lattice of Bose–Einstein condensates