  We propose a scheme able to generate on demand a steady-state entanglement
between two non-degenerate cavity modes. The scheme relies on the interaction
of the cavity modes with driven two or three-level atoms which act as a coupler
to build entanglement between the modes. We show that in the limit of a strong
driving, crucial for the generation of entanglement between the modes is to
imbalance populations of the dressed states of the driven atomic transition. In
the case of a three-level V-type atom, we find that a stationary entanglement
can be created on demand by tuning the Rabi frequency of the driving field to
the difference between the atomic transition frequencies. The resulting
degeneracy of the energy levels together with the spontaneously generated
coherence generates a steady-state entanglement between the cavity modes. It is
shown that the condition for the maximal entanglement coincides with the
collapse of the atomic system into a pure trapping state. We also show that the
creation of entanglement depends strongly on the mutual polarization of the
transition atomic dipole moments.
