  We analyse the possibilities for quantum state engineering offered by a model
for Kerr-type non-linearity enhanced by electromagnetically induced
transparency (EIT), which was recently proposed by Petrosyan and Kurizki [{\sl
Phys. Rev. A} {\bf 65}, 33833 (2002)]. We go beyond the semiclassical treatment
and derive a quantum version of the model with both a full Hamiltonian approach
and an analysis in terms of dressed states. The preparation of an entangled
coherent state via a cross-phase modulation effect is demonstrated. We briefly
show that the violation of locality for such an entangled coherent state is
robust against low detection efficiency. Finally, we investigate the
possibility of a bi-chromatic photon blockade realized via the interaction of a
low density beam of atoms with a bi-modal electromagnetic cavity which is
externally driven. We show the effectiveness of the blockade effect even when
more than a single atom is inside the cavity. The possibility to control two
different cavity modes allows some insights into the generation of an entangled
state of cavity modes.
