  We study ground states of two-component condensates in a harmonic trap. We
prove that in the strongly coupled and weakly interacting regime, the two
components segregate while a symmetry breaking occurs. More precisely, we show
that when the intercomponent coupling strength is very large and both
intracomponent coupling strengths are small, each component is close to the
positive or the negative part of a second eigenfunction of the harmonic
oscillator in $\R^2$. As a result, the supports of the components approach
complementary half-spaces, and they are not radially symmetric.
