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.
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