Interaction of two quantum dots mediated by edge modes of coupled-cavity arrays

Topological photonics is a hot topic in recent years. We combine it with the quantum optics and explore the dynamics of two quantum dots (QDs) separated by the finite coupled-cavity arrays (CCAs). The finite CCAs possessing the alternating hopping strengths will lead to the existence of the topological protected edge modes, also called zero energy modes, when the boundaries leave the weak hopping at two ends. Due to the two edge modes, i.e., symmetric and antisymmetric, with nearly degenerate frequencies, the dynamics of two QDs coupled to the cavities at both ends exhibit complicated behaviors. When the CCAs are composed of a large number of cavities, there are two kinds of phenomena: if the coupling between QDs and cavity is weak, two edge modes will cancel each other out and isolate two QDs deeply; if the coupling between QDs and cavities is large compared with hopping strength, the edge mode disappears and two QDs can be connected through extend modes. Importantly, when the CCAs are formed by a small number of cavities, energy can be transferred to each other between two QDs through the edge modes. Such energy transfer is topologically protected, and the period is long and easily controlled. We also investigate the effects of topologically protected quantum entangled states on such system and find that the quantum entanglement can be well kept or generated for appropriate choices of system parameters and initial states. The investigations enrich the manifestation of topological physics and are helpful to apply the topological protection to quantum computation and quantum communication.