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An on-going challenge within scalable optical quantum information processingis to increase the collection efficiency $\varepsilon$ and the photonindistinguishability $\eta$ of the single-photon source towards unity. Withinquantum dot-based sources, the prospect of increasing the product $\varepsilon\eta$ arbitrarily close to unity was recently questioned. In this work, wediscuss the influence of the trade-off between efficiency andindistinguishability in the presence of phonon-induced decoherence, and we showthat the photonic "hourglass" design allows for improving $\varepsilon \eta$beyond the predicted maximum for the standard micropillar design subject tothis trade-off. This circumvention of the trade-off is possible thanks tocontrol of the spontaneous emission into background radiation modes, and ourwork highlights the importance of engineering of the background emission infuture pursuits of near-unity performance of quantum dot single-photon sources.

Near-unity efficiency and photon indistinguishability for the "hourglass" single-photon source using suppression of background emission