  We consider a Bose-Einstein condensate (BEC) of $^7Li$ in a situation where
the density undergoes a symmetry breaking in real space. This occurs for a
suitable number of condensed atoms in a double well potential, obtained by
adding a standing wave light field to the trap potential. Evidence of
bistability results from the solution of the Gross-Pitaevskii equation. By
second quantization, we show that the classical bistable situation is in fact a
Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC
states. The oscillation between the two states is called MQC (macroscopic
quantum coherence); we study the effects of losses on MQC.
