  We study the mutual interaction between two identical quantum dots coupled to
the normal modes of two-site photonic crystal molecules in a planar waveguide
geometry, i.e. photonic crystal dimers. We find that the radiative coupling
between the two quantum emitters is maximized when they are in resonance with
either the bonding or the antibonding modes of the coupled cavity system.
Moreover, we find that such effective interdot coupling is sizable, in the meV
range, and almost independent from the cavities distance, as long as a normal
mode splitting exceeding the radiative linewidth can be established (strong
cavity-cavity coupling condition). In realistic and high quality factor
photonic crystal cavity devices, such distance can largely exceed the emission
wavelength, which is promising for long distance entanglement generation
between two qubits in an integrated nanophotonic platform. We show that these
results are robust against position disorder of the two quantum emitters within
their respective cavities.
