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arXiv:1705.10953 · Physical Review A

Effects of filtering on the purity of heralded single photons from parametric sources

Daniel R. Blay, Michael J. Steel, L. G. Helt

Published Nov 20, 2017• 22 citations
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Abstract

Optical quantum protocols are reliant on the production of highly pure single photons. However, most parametric heralded single-photon sources possess spectral correlations, limiting the purity of the produced photon. The most common method for restoring the purity is with narrowband spectral filtering, which comes at the cost of reducing the rate of heralding detection. Here, we characterize this trade-off analytically for a large class of parametric sources. It is possible to achieve up to 20% heralding success probabilities with 90% heralded photon purities.

DOI
10.1103/physreva.96.053842

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Optical quantum protocols are reliant on the production of highly pure single photons. However, most parametric heralded single-photon sources possess spectral correlations, limiting the purity of the produced photon. The most common method for restoring the purity is with narrowband spectral filtering, which comes at the cost of reducing the rate of heralding detection. Here, we characterize this trade-off analytically for a large class of parametric sources. It is possible to achieve up to 20% heralding success probabilities with 90% heralded photon purities.
Many quantum information protocols require the high rate production of individual photons with near unit purity. The most mature platform for producing these photons is nonlinear optical sources, which exploit parametric processes to produce photon pairs, one of which is subsequently detected to “herald” the presence of its partner. The photon pairs produced in such sources often have strong frequency correlations, which adversely affect the purity of the heralded single photons, and so such sources are spectrally filtered to restore the purity. Because this process throws away photons, the rate of photon production is reduced - filtering increases purity at the cost of efficiency. This relationship has been explored extensively numerically [1-3], but has not been well understood analytically. As the demand for multi-photon experiments increases, it is becoming necessary to precisely quantify the trade-off between purity and efficiency. We believe our work enables this.
Photon pairs produced by parametric down-conversion or four-wave mixing can interfere with each other in multiport interferometers or carry entanglement between distant nodes for use in entanglement swapping. This requires the photons to be spectrally pure to ensure good interference and have high heralding efficiency to know accurately the number of photons involved and to maintain high rates as the number of photons grows. Spectral filtering is often used to remove noise and define spectral properties. For heralded single photons high purity and heralding efficiency are possible by filtering the heralding arm, but when both photons in typical pair sources are filtered, we show that the heralding efficiency of one or both of the photons is strongly reduced even by ideal spectral filters with 100% transmission in the passband: any improvement in reduced-state spectral purity from filtering comes at the cost of lowered heralding efficiency. We consider the fidelity to a pure, lossless single photon, symmetrize it to include both photons of the pair, and show this quantity is intrinsically limited for sources with spectral correlation. We then provide a framework for this effect for benchmarking common photon-pair sources and present an experiment where we vary the photon filter bandwidths and measure the increase in purity and corresponding reduction in heralding efficiency.
One method to produce pure heralded single photons (HSP) when using the optical process of spontaneous parametric down-conversion (SPDC) is by modifying the joint spectrum of the photon pairs by means of spectral filters. In this work, we characterize the dependence, with the bandwidth of such filters, of the spectral purity and heralding efficiency of the HSP generated in a bulk SPDC. The values we report for the purity and heralding efficiency are obtained from measurements of the joint spectrum. Our results are in agreement with the theoretical model that predicts a trade-off between the purity and heralding efficiency, and they complement similar measurements that have been done for HSP produced by other types of sources.
A major obstacle to a practical, heralded source of single photons is the fundamental trade-off between high purity and high production rate. To overcome this difficulty, we propose applying sequential spectral and temporal filtering on the signal photons before they are detected for heralding. Based on a multimode theory that takes into account the effect of simultaneous multiple photon-pair emission, we find that these filters can be optimized to yield both high purity and a high production rate. While the optimization conditions vary depending on the underlying photon-pair spectral correlations, all correlation profiles can lead to similarly high performance levels when optimized filters are employed. This suggests that a better strategy for improving the performance of heralded single-photon sources is to adopt an appropriate measurement scheme for the signal photons, rather than tailoring the properties of the photon-pair generation medium.
Sources of single photons in pure quantum states are essential to many quantum optics applications. We explore a technique, known as group-velocity matching, that enables the heralded generation of pure single photons through nonlinear optical processes. It reduces or eliminates the requirement of spectral filtering that conventional sources rely on to achieve high purity, therefore increasing both heralding efficiency and photon flux. Implementation in both spontaneous parametric downconversion and spontaneous four-wave mixing is studied as we discuss several recent experimental realizations demonstrating purity of more than 0.84 for the heralded photons.