Phonon approach to an array of traps containing Bose-Einstein condensates

We investigate theoretically an array of traps containing Bose-Einstein condensates, taking into account tunneling of atoms between adjacent traps and atom-atom interactions within each trap. After an expansion valid in the limit of a large number of atoms, we end up studying a variation of the problem of phonons in a one-dimensional lattice. Analysis of these fictitous phonons and their vacua shows that the fluctuations in atom numbers and phases of the condensates behave qualitatively as in the much-studied case of two traps.