  The availability of Bose-Einstein condensates as mesoscopic or macroscopic
quantum objects has aroused new interest in the possiblity of making and
detecting coherent superpositions involving many atoms. In this article we show
that it may be possible to generate such a superposition state in a reasonably
short time using Feshbach resonances to tune the inter-atomic interactions in a
double-well condensate.
  We also consider the important problem of distinguishing whether a coherent
superposition or a statistical mixture is generated by a given experimental
procedure. We find that unambiguously distinguishing even a perfect `NOON'
state from a statistical mixture using standard detection methods will present
experimental difficulties.
