The generalized purity is employed for investigating the process of coherence loss and delocalization of the $Q$ function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles $\left(N\right)$. A power-law dependence of the critical parameter with $N$ is derived.

• Received 20 December 2008

DOI:https://doi.org/10.1103/PhysRevA.80.013610