  We discuss theoretically the ground state of a Bose-Einstein condensate with
attractive atom-atom interactions in a double-well trap as a starting point of
Heisenberg-limited atom interferometry. The dimensionless parameter governing
the quality of the ground state for this purpose is identified. The
near-degeneracy between the ground state and the first excited state severely
curtails the prospects of the thermally prepared ground state in quantum
metrology.
