Radiative coupling between quantum dots in photonic crystal molecules

Abstract

In the present work, we theoretically address the possibility of usingstrongly coupled photonic crystal molecules to efficiently increasethe mutual coupling rate between two quantum dots at large interdotdistances. The photonic molecules we are interested in are composedof two coupled photonic crystal slab cavities, or photonic crystaldimers. We specifically consider coupled L3 cavities, i.e., threemissing holes in a hexagonal lattice. We treat the light-matter couplingwith a semiclassical formalism based on Greens tensors andthe classical electromagnetic fields are solved within a guided-modeexpansion approach. We find that when the quantum dots are in resonance with either of the two lowest energy modes (bonding/antibonding) of the photonic dimer, and in the strong cavity-cavity coupling regime, the inter-dot radiative coupling strength is proportional to the quality factors of the dimer modes and it can be of the orde of 1 meV, which is at least an order of magnitude larger than typicalvalues achieved in one-dimensional systems. We also address theeffects of structural disorder in the photonic crystal lattice on the mutualcoupling between the two quantum dots, by assuming disorderparameters that are consistent with the current state-of-art fabricationtechnology. We find that the effective radiative coupling between thedots is robust against non-perfect quantum dot positioning and, to asmaller extent, to structural disorder in the photonic crystal. Using afully quantum mechanical model, based on the master equation, wequantify the entanglement between the quantum dots by the Peres-Horodecki negativity criterion. We show that it is possible to achievenegativity values of the order of 0.1 (20% of the maximum value) inthe steady sate regime, for interdot distances which are larger thanthe characteristic wavelength of the system. We also find that thisamount of entanglement remains of the same order of magnitude, aslong as the distance between the dots is such that the normal modesplitting of the photonic dimer is much greater than the normal modelinewidth. Considering detuned quantum dots, we find that the entanglement is preserved as long as the dot-dot detuning is smallerthan the exciton linewidth. Finally, we determine that the most appropriateconfiguration for long-range entanglement applications isthe one for which the line connecting the centers of the L3 cavitiesis at an angle of 30 degrees with the horizontal axis. Based on thisconfiguration, we propose a simple device for practical applicationsin the transient dynamics where the amount of entanglement can beof the order of 40% for state-of-art InGaAs quantum dots.