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We study the collapse and revival of interference patterns in the momentumdistribution of atoms in optical lattices, using a projection technique toproperly account for the fixed total number of atoms in the system. We considerthe common experimental situation in which weakly interacting bosons are loadedinto a shallow lattice, which is suddenly made deep. The collapse and revivalof peaks in the momentum distribution is then driven by interactions in alattice with essentially no tunnelling. The projection technique allows to usto treat inhomogeneous (trapped) systems exactly in the case thatnon-interacting bosons are loaded into the system initially, and we usetime-dependent density matrix renormalization group techniques to study thesystem in the case of finite tunnelling in the lattice and finite initialinteractions. For systems of more than a few sites and particles, we find goodagreement with results calculated via a naive approach, in which the state ateach lattice site is described by a coherent state in the particle occupationnumber. However, for systems on the order of 10 lattice sites, we findexperimentally measurable discrepancies to the results predicted by thisstandard approach.

Atomic matter-wave revivals with definite atom number in an optical lattice