The proposal is a continuation of work on phase engineering of non-linear structures, and highly entangled number states in gaseous atomic Bose-Einstein condensates, or BECs, and proposals for work, growing out of this, in the actualities of detection of such entangled states, and the masurement of the relative phase of quantum macroscopic superposition states. In addition, the PI is developing a combined computational theory which includes "full" mean field effects, through solution of coupled GP (Gross-Piteavskii) equations, and simultaneously full (or approximate for more than two well traps) treatment of correlations, so that phase relations between split" condensates are properly maintained, and the coherent and entangled states needed for Heisenberg limited measurements can be described. Correct treatment of both correlation and mean-field effects is computationally and intellectually intensive, but necessary for modeling current experiments, as well as making realistic predictions of condensate behavior.
