  Quantum superpositions of macroscopically distinguishable states having
distinct phases can be created with a Bose-Einstein condensate trapped in a
periodic potential. The experimental signature is contained in the phase
distribution of the interference patterns obtained after releasing the traps.
Moreover, in the double well case, this distribution exhibits a dramatic
dependence on the parity of the total number of atoms. We finally show that,
for single well occupations up to a few hundred atoms, the macroscopic quantum
superposition can be robust enough against decoherence to be experimentally
revealable within current technology.
