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Conservation of the total isotopic spin S of a two-component Bose gas-like$^{87}$Rb-has a dramatic impact on the structure of the ground state. In thecase when S is much smaller than the total number of particles N, thecondensation of each of the two components occurs into two single-particlemodes. The quantum wavefunction of such a groundstate is a Schr\"odinger Cat-asuperposition of the phase separated classical condensates, the most "probable"state in the superposition corresponding to the classical groundstate in thesector of given N and S. After measurement of the spatial distribution of thedensities of the two components, the Cat collapses into one of the classicalcondensate states.Comment: 5 RevTex pages, no figures; replaced with revised version, where the  discussion on stability against temporal white noise and losses is adde

Ground States of SU(2)-Symmetric Confined Bose Gas: Quantum Superposition of the Phase-Separated Classical Condensates