Design of bright, fiber-coupled and fully factorable photon pair sources

From quantum computation to quantum key distribution, many quantumenhanced applications rely on the ability to generate pure single-photons. Even though the process of spontaneous parametric downconversion is widely used as the basis for photon-pair sources, the conditions for pure heralded single-photon generation, taking into account both spectral and spatial degrees of freedom, have not been fully described. We present an analysis of the spatio-temporal correlations present in photon pairs produced by type-I, non-collinear spontaneous parametric downconversion. We derive a set of conditions for full factorability in all degrees of freedom – required for the heralding of pure heralded single photons – between the signal and idler modes. In this paper we consider several possible approaches for the design of bright, fiber-coupled, and factorable photon-pair sources. We show through numerical simulations of the exact equations that sources based on: i) the suppression of spatio-temporal entanglement according to our derived conditions, and ii) a tightly-focused pump beam together with optimized fiber-collection modes and spectral filtering of the signal and idler photon pairs, lead to a source brightness of the same order of magnitude. Likewise, we find that both of these sources lead to a drastically higher factorable photon-pair flux, compared to an unengineered source. Design of bright, fiber-coupled and fully factorable photon pair sources 2