Can macroscopic quantum superposition states (or highly entangled number states) be observed directly\u27? Specifically, can phase contrast imaging be applied to observe a superposition state with essentially all of the atoms in a gaseous double well BEG being simultaneously in both wells at the same time\u27? That is we are looking to image states of the type vertical bar N, 0 \u3e +vertical bar 0, N \u3e where vertical bar L, R \u3e denotes L particles in the Left well and R. in the Right. We will happily settle for states of the form IN n, n \u3e +In, N is \u3e, with 71, \u3c\u3c N, these being less ephemeral. Earlier work in our group, Perry, Reinhardt and Kahn, has shown that such highly entangled number states may be generated by appropriate phase engineering, just as in the case of the phase engineering of solitons in single well BECs. Experimentalists have been hesitant to attempt to create such states in fear that definitive observations cannot be carried out. There have also been suggestions that Nature will prevent such superpositions from existing for N too large... and thus there are also basic issues in quantum theory which may prevent the formation and detection of such states. In the present progress report we begin an investigation of calculating the lifetimes of such entangled states in the presence of both observation and spontaneous decay both of which perturb, and eventually destroy, the entanglement under investigation via quantum back-action. Quantum State Diffusion (QSD) provides a useful computational tool in addressing such questions, and we present the initial results of exploring this novel use of QSD
