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We show that two spatially separated semiconductor quantum dots underresonant and continuous-wave excitation can be strongly entangled in thesteady-state, thanks to their radiative coupling by mutual interaction throughthe normal modes of a photonic crystal dimer. We employ a quantum masterequation formalism to quantify the steady-state entanglement by calculating thesystem {\it negativity}. Calculations are specified to consider realisticsemiconductor nanostructure parameters for the photonic crystal dimer-quantumdots coupled system, determined by a guided mode expansion solution of Maxwellequations. Negativity values of the order of 0.1 ($20\%$ of the maximum value)are shown for interdot distances that are larger than the resonant wavelengthof the system. It is shown that the amount of entanglement is almostindependent of the interdot distance, as long as the normal mode splitting ofthe photonic dimer is larger than their linewidths, which becomes the onlyrequirement to achieve a local and individual qubit addressing. Consideringinhomogeneously broadened quantum dots, we find that the steady-stateentanglement is preserved as long as the detuning between the two quantum dotresonances is small when compared to their decay rates. The steady-stateentanglement is shown to be robust against the effects of pure dephasing of thequantum dot transitions. We finally study the entanglement dynamics for aconfiguration in which one of the two quantum dots is initially excited andfind that the transient negativity can be enhanced by more than a factor of twowith respect to the steady-state value. These results are promising forpractical applications of entangled states at short time scales.

Steady-state entanglement between distant quantum dots in photonic crystal dimers