Spatial compression of a particle state in a parabolic potential by spin   measurements
  We propose a scheme for engineering compressed spatial states in a two-dimensional parabolic potential with a spin-orbit coupling by selective spin measurements. This sequence of measurements results in a coordinate-dependent density matrix with probability maxima achieved at a set of lines or at a two dimensional lattice. The resultant probability density depends on the spin-orbit coupling and the potential parameters and allows one to obtain a broad class of localized pure states on demand. The proposed scheme can be realized in spin-orbit coupled Bose-Einstein condensates. 
P. V. Pyshkin, E. Ya. Sherman, Da-Wei Luo, J. Q. You, and Lian-Ao Wu
cond-mat.other quant-ph