  Effective models of hard-core hole pair bosons and triplets are derived from
the t-J model in ladders and on the square lattice by performing a change from
site to dimer basis. The Hilbert space is truncated by projecting out
single-occupied electron states and only nearest neighbor interactions are
retained. The resulting effective models in one and two dimensions are studied
by numerical techniques. In both spatial dimensions, the main result is that
each hole pair is surrounded by a singlet cloud expelling triplet excitations
from its vicinity. It is suggested an interpretation of this feature as a phase
separated state between a hole-pair rich singlet phase and an undoped triplet
phase with antiferromagnetic correlations. The possible relevance of this
result to other theoretical scenarios and experimental results is discussed.

Superconductivity