  We study the normal modes and the stability of two component condensates in a
phase separated regime. In such a regime the system can undergo a quantum phase
transition upon the change of interaction strength between bosons of the same
species or the variation of the trap frequencies. 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 the interface
tension and the phase diagram. The symmetric to asymmetric transition is the
simplest quantum phase transition that one can imagine. We found new branches
of normal modes which are specific for trapped multicomponent condensates and
are analogous to the waves at the interface between two layers of immiscible
fluids under gravity. At the point of the phase transition the frequencies of
those modes go to zero and become imaginary which causes an instability. The
interface tension shifts the normal mode frequencies and changes the stability
region of the system.
