  We investigate the ground state properties of the $t-J$ model on a two leg
ladder with anisotropic couplings ($t,\alpha=J/t$) along rungs and
($t',\alpha'=J'/t'$) along legs. We have implemented a cluster approach based
on 4-site plaqettes. In the strong asymmetric cases $\alpha/\alpha'\ll 1$ and
$\alpha'/\alpha\ll 1$ the ground state energy is well described by plaquette
clusters with charges $Q=2,4$. The interaction between the clusters favours the
condensation of plaquettes with maximal charge -- a signal for phase
separation. The dominance of Q=2 plaquettes explains the emergence of tightly
bound hole pairs. We have presented the numerical results of exact
diagonalization to support our cluster approach.

Strongly Correlated Electrons