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arXiv:0807.1725 · Physical Review A

Coherence measures for heralded single-photon sources

Erwann Bocquillon, Christophe Couteau, Mohsen Razavi, Raymond Laflamme, Gregor Weihs

Published Mar 18, 2009• 88 citations
arXivHTMLPDF

Abstract

Single-photon sources (SPSs) are mainly characterized by the minimum value of their second-order coherence function, viz. their ${g}^{(2)}$ function. A precise measurement of ${g}^{(2)}$ may, however, require high time-resolution devices, in whose absence, only time-averaged measurements are accessible. These time-averaged measures, standing alone, do not carry sufficient information for proper characterization of SPSs. Here, we develop a theory, corroborated by an experiment, which allows us to scrutinize the coherence properties of heralded SPSs that rely on continuous-wave parametric down conversion. Our proposed measures and analysis enable proper standardization of such SPSs.

DOI
10.1103/physreva.79.035801

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Comment on “Coherence measures for heralded single-photon sources”

Stefano Bettelli

A recent Brief Report [Phys. Rev. A 79, 035801 (2009)] investigates two figures of merit for heralded photon sources based on spontaneous parametric down-conversion with a continuous pump, namely, the time-averaged temporal coherence between the signal and idler beams and the time-averaged conditioned second-order degree of coherence for photons in the heralded arm. However, contrary to what is claimed, no one-arm second-order effect is actually measured.

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Single-photon sources (SPSs) are mainly characterized by the minimum value of their second-order coherence function, viz. their g(2){g}^{(2)}g(2) function. A precise measurement of g(2){g}^{(2)}g(2) may, however, require high time-resolution devices, in whose absence, only time-averaged measurements are accessible. These time-averaged measures, standing alone, do not carry sufficient information for proper characterization of SPSs. Here, we develop a theory, corroborated by an experiment, which allows us to scrutinize the coherence properties of heralded SPSs that rely on continuous-wave parametric down conversion. Our proposed measures and analysis enable proper standardization of such SPSs.
Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its g (2) function. An accurate measurement of such coherence functions commonly requires high-precision single-photon detectors, in whose absence only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors—i.e., the multiple-photon emissions of the source, the time resolution of photodetectors and our chosen width of coincidence window—our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step towards the standardization of such heralded single-photon sources.
Single photons exhibit nonclassical, counterintuitive behavior that can be exploited in the developing field of quantum technology. They are needed for various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. This drives the current intensive research into the realization of true deterministic sources of single photons on demand. Lacking such a source, many researchers default to the well-established workhorse: spontaneous parametric down-conversion that generates entangled signal-idler pairs. Since this source is thermal statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a heralded second-order coherence function of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photon-resolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signal-photon state alone.
Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down-conversion combined with a heralding photon detection. The heralded light pulse from such a source is typically treated as single mode; this treatment, however, is incomplete. We develop a full multimode description based on the exact Bogoliubov treatment of the down-conversion process. We then provide a perturbative and effective treatment, which illustrates the most important physical mechanisms and permits analytical estimates of the success probability and purity of single-photon states under practical heralding conditions, both without relying on the precise detection time of the heralding photon and when accepting photons only in a narrow window around the time of the detection. This permits us to characterize the emitted light under three different assumptions for the pump pulse. For spontaneous parametric down-conversion with a very short pump pulse, we find the single-mode description to be accurate, while for longer pump pulses and continuous pumping, a multimode description is necessary. Our findings can be used to guide the design of quantum information protocols based on heralded single-photon sources, as their performance may depend on the multimode nature of the sources.
Low-photon-number sources can exhibit non-classical, counterintuitive behavior that can be exploited in the developing field of quantum technology. Single photons play a special role in this arena since they represent the ultimate lowphoton- number source. They are considered an important element in various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. True deterministic sources of single photons on demand are currently an area of intensive research, but have not been demonstrated in a practical setting. As a result, researchers commonly default to the well-established workhorse: spontaneous parametric down-conversion generating entangled signal-idler pairs. Since this source is thermal-statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a "heralded second-order coherence function" of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work, we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photonresolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signalphoton state alone.
Single Photon Sources (SPSs) play a pivotal role in fields such as quantum communication and quantum cryptography by generating information in a secure manner. However, realizing the ideal emission of single photons with high efficiency is still a theoretical model. This leads to the presence of multiphoton components in SPSs, which could potentially compromise security. This study focuses on enhancing the purity of a class of sources by characterizing their photon number distribution and mitigating the impact of the multiphoton components. We propose the use of Photon Number Resolving Detectors (PNRD) as a technique to exclude multiphoton contributions, particularly in sources like Spontaneous Parametric Down Conversion sources, where emitted photons can be represented as Two-Mode Squeezed Vacuum states. By analyzing the second-order cross-correlation function, g2(0), using either PNRD or Single Photon Detectors, we can quantify the reduction in multiphoton contributions.