Many-body state engineering using measurements and fixed unitary   dynamics
  We develop a scheme to prepare a desired state or subspace in high-dimensional Hilbert-spaces using repeated applications of a single static projection operator onto the desired target and fixed unitary dynamics. Benchmarks against other control schemes, performed on generic Hamiltonians and on Bose-Hubbard systems, establish the competitiveness of the method. As a concrete application of the control of mesoscopic atomic samples in optical lattices we demonstrate the near deterministic preparation of Schr\"{o}dinger cat states of all atoms residing on either the odd or the even sites. 
Mads Kock Pedersen, Jens Jakob W. H. S{\o}rensen, Malte C. Tichy,   Jacob F. Sherson
quant-ph