  We study the possibility to create many-particle Schr\"odinger cat-like
states by using a Feshbach resonance to reverse the sign of the scattering
length of a Bose-Einstein condensate trapped in a double-well potential. To
address the issue of experimental verification of coherence in the cat-like
state, we study the revival of the initial condensate state in the presence of
environmentally-induced decoherence. As a source of decoherence, we consider
the interaction between the atoms and the electromagnetic vacuum, due to the
polarization induced by an incident laser field. We find that the resulting
decoherence is directly related to the rate at which spontaneously scattered
photons carry away sufficient information to distinguish between the two
atom-distributions which make-up the cat state. We show that for a 'perfect'
cat-state, a single scattered photon will bring about a collapse of the
superposition, while a less-than-perfect cat-like state can survive multiple
scatterings before collapse occurs. In addition, we study the dephasing effect
of atom-atom collisions on the cat-like states.
