Abstract
From quantum computation to quantum key distribution, many quantum-enhanced applications rely on the ability to generate pure single photons. Even though the process of spontaneous parametric downconversion (SPDC) 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 SPDC. We derive a set of conditions for full factorability in all degrees of freedom—required for the heralding of pure 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.
Highlights
To bright sources of fiber-coupled photon pairs, which exhibit factorability in all photonic degrees of freedom
In order to compare the performance of various sources of interest, we present the results of numerical simulations leading to values for the heralded single-photon purity and the source brightness
We consider two additional variants: (i) an unengineered source for which the fiber-coupled signal and idler modes are spectrally filtered to render the photon pairs nearly factorable, and (ii) in addition to the presence of spontaneous parametric downconversion (SPDC) spectral filtering, the pump beam is focused to the same degree as for the engineered source, and the width of the fiber collection modes is optimized for maximum source brightness
Summary
We consider for the present analysis a type-I, non-collinear source of SPDC photon pairs. We model the broadband pump beam as a chromatic superposition of single-frequency Gaussian beams, with a coincident beamwaist of radius w0 and a coincident central direction of. Fiber-collection modes are described by Gaussian beams, with their beam waists at the output face of the nonlinear crystal. Φ0 indicates the azimuthal orientation of the detection plane formed by the central directions of propagation of the two fiber-collection modes The coordinate system to be used is chosen so that the z-axis is parallel to the pump beam and the y-axis is parallel to the projection of the pump walk-off direction along the transverse plane (see figure 1(b)). φ0 indicates the azimuthal orientation of the detection plane formed by the central directions of propagation of the two fiber-collection modes
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