  We investigate an attractive atomic Bose-Einstein condensate (BEC) trapped by
a double-well potential in the axial direction and by a harmonic potential in
the transverse directions. We obtain numerically, for the first time, a quantum
phase diagram which includes all the three relevant phases of the system:
Josephson, spontaneous symmetry breaking (SSB), and collapse. We consider also
the coherent dynamics of the BEC and calculate the frequency of
population-imbalance mode in the Josephson phase and in the SSB phase up to the
collapse. We show that these phases can be observed by using ultracold vapors
of 7Li atoms in a magneto-optical trap.
