Revealing Single-Trap Condensate Fragmentation by Measuring Density-Density Correlations after Time of Flight

We consider ultracold bosonic atoms in a single trap in the Thomas-Fermi regime, forming many-body states corresponding to stable macroscopically fragmented two-mode condensates. It is demonstrated that upon free expansion of the gas, the spatial dependence of the density-density correlations at late times provides a unique signature of fragmentation. This hallmark of fragmented condensate many-body states in a single trap is due to the fact that the time of flight modifies the correlation signal such that two opposite points in the expanding cloud become uncorrelated, in distinction to a nonfragmented Bose-Einstein condensate, where they remain correlated.