Interferometry with independently prepared Bose-Einstein condensates

We show that it is possible to reach the sub shot-noise sensitivity of the phase estimation using two independently prepared Bose-Einstein condensates as an input of an interferometer. In this scenario, the quantum correlations between the particles, which are necessary to beat the shot-noise limit, arise from the indistinguishability of bosons. Allowing for atom number fluctuations independently in each condensate, we calculate the ultimate bound of the sensitivity. Our main conclusion is that even in presence of major atom number fluctuations, an interferometer operating on two independent condensates can give very high sensitivity. We also show that the estimation from the measurement of the number of atoms utilizes these quantum correlations. This observation, in context of recent measurement of the Fisher information in a many-body system [H. Strobel {\it et al}, Science {\bf 345}, 424 (2014)], opens the way towards the construction of a new type of an interferometer operating below the shot-noise limit.