Atomic matter-wave revivals with definite atom number in an optical   lattice
  We study the collapse and revival of interference patterns in the momentum distribution of atoms in optical lattices, using a projection technique to properly account for the fixed total number of atoms in the system. We consider the common experimental situation in which weakly interacting bosons are loaded into a shallow lattice, which is suddenly made deep. The collapse and revival of peaks in the momentum distribution is then driven by interactions in a lattice with essentially no tunnelling. The projection technique allows to us to treat inhomogeneous (trapped) systems exactly in the case that non-interacting bosons are loaded into the system initially, and we use time-dependent density matrix renormalization group techniques to study the system in the case of finite tunnelling in the lattice and finite initial interactions. For systems of more than a few sites and particles, we find good agreement with results calculated via a naive approach, in which the state at each lattice site is described by a coherent state in the particle occupation number. However, for systems on the order of 10 lattice sites, we find experimentally measurable discrepancies to the results predicted by this standard approach. 
J. Schachenmayer, A. J. Daley, and P. Zoller
cond-mat.quant-gas