Huge quantum particle number fluctuations in a two-component Bose gas in a double-well potential

Two component Bose gas in a double well potential with repulsive interactions may undergo a phase separation transition if the inter-species interactions outweigh the intra-species ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components. That is, probability for observation of any mixture of particles in each potential well becomes uniform.