  We propose a new kind of quantum phase transition in phase separated mixtures
of Bose-Einstein condensates. In this transition, the distribution of the two
components changes from a symmetric to an asymmetric shape. We discuss the
nature of the phase transition, the role of interface tension and the phase
diagram. The symmetric to asymmetric transition is the simplest quantum phase
transition that one can imagine. Careful study of this problem should provide
us new insight into this burgeoning field of discovery.
