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

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