Planck-Scale Traces from the Interference Pattern of two Bose-Einstein Condensates

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We analyze the possible effects arising from Planck scale regime upon the interference pattern of two non-interacting Bose-Einstein condensates. We start with the analysis of the free expansion of a condensate, taken into account the effects produced by a deformed dispersion relation, suggested in several quantum-gravity models. The analysis of the condensate free expansion, in particular, the modified free velocity expansion, suggests in a natural way, a modified uncertainty principle that could leads to new phenomenological implications related to the quantum structure of space time. Finally, we analyze the corresponding separation between the interference fringes after the two condensates overlap, in order to explore the sensitivity of the system to possible signals caused by the Planck scale regime.