Bistability and macroscopic quantum coherence in a BEC of ^7Li

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.