Ultimate photon entanglement in biexciton cascade

Abstract: The polarization entanglement of photons emitted by semiconductor quantum dots is unavoidably limited by the spin fluctuations of the host lattice nuclei. To overcome this limitation, we develop a theory of entangled photon pair generation by a symmetric colloidal quantum dot mediated by a triplet exciton. We derive general analytical expressions for the concurrence as a function of the hyperfine interaction strength and show that it is intrinsically higher than that in conventional doublet-exciton systems such as self-assembled quantum dots. The concurrence sensitively depends on the shape anisotropy and the strain applied to a nanocrystal. In particular, we uncover a possibility of completely suppressing the detrimental effect of the hyperfine interaction due to the interplay between nanocrystal anisotropy and electron-hole exchange interaction. We argue that this represents the ultimate limit for the generation of entangled photon pairs by semiconductor quantum dots.