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arXiv:2107.03468 · Physical Review A

Heralding on the detection of zero photons

Cory M. Nunn, J. D. Franson, T. B. Pittman

Published Sep 30, 2021• 27 citations
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Abstract

Although heralding signals in quantum optics experiments are typically based on the detection of exactly one photon, it has recently been theoretically shown that heralding based on the detection of zero photons can be useful in a number of quantum information applications. Here we experimentally investigate a technique for ``heralding on zero photons'' using conventional single-photon detectors. We illustrate how detector efficiency and dark count rates play a counterintuitive role in the ability to accurately detect zero photons, and we use a variant of the Hong-Ou-Mandel interferometer to study the deleterious effects of limited detector efficiency when heralding on zero.

DOI
10.1103/physreva.104.033717

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Although heralding signals in quantum optics experiments are typically based on the detection of exactly one photon, it has recently been theoretically shown that heralding based on the detection of zero photons can be useful in a number of quantum information applications. Here we experimentally investigate a technique for ``heralding on zero photons'' using conventional single-photon detectors. We illustrate how detector efficiency and dark count rates play a counterintuitive role in the ability to accurately detect zero photons, and we use a variant of the Hong-Ou-Mandel interferometer to study the deleterious effects of limited detector efficiency when heralding on zero.
We consider photon heralding with quasi-number-resolving detection schemes and account for detection efficiencies and dark count probabilities. With a straightforward formalism, we develop closed-form expressions for the heralding probability, photon number distribution of the resulting heralded state, and fidelity of this heralded state to a single-photon state. We calculate that this fidelity has a maximum as a function of the number of multiplexed detection modes and that, for experimental configurations in which the maximum is reached for quite a large number of detection modes, it can still be highly beneficial to multiplex fewer modes.
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.
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.
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involve maximizing the interference visibility while maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include a large number of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong–Ou–Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced.
Interference between independent photon sources is the key technique to realize complex quantum systems for more sophisticated applications such as multi-photon entanglement generation and quantum teleportation. Here, we report Hong-Ou-Mandel interference (HOMI) between two independent 1.55 m all-fiber photon pair sources over two 100 GHz dense wave division multiplexing (DWDM) channels, whose visibility reaches 53.2%8.4% (82.9%5.3%) without (with) back ground counts subtracted. In addition, we theoretically describe in detail the single photon spectral purity of the photon source generated in dispersion shifted fiber (DSF), simulate the influences of the pulse width and filter bandwidth on the purity, and obtain the optimized condition. The optimized pump pulse width is 8 ps and filter bandwidth is about 40 GHz or less. A home-made 1550.1 nm mode-locked fiber laser source, whose pulse width and repetition rate are 25 ps and 27.9 MHz respectively, acts as a pump of photon source. A tunable attenuator is used to adjust the pump power of the photon source, and the broad band background fluorescence photons are filtered out by cascade 100 GHz DWDM filters. The clean pump beam is divided into two equal parts by the 50 : 50 optical coupler to pump two 300 m DSFs (cooled by liquid nitrogen) to generate independent photon sources. Then the strong pump beam and noise photon from Raman scattering in orthogonal polarization are removed by 2 groups of 200 GHz DWDM filters and fiber polarization rotator and polarizer. Then two 100 GHz DWDMs are used for separating photons at correlated channel pairs. The relative delay between the two independent photons is adjusted by tunable fiber delay line. Photons from the same channels are combined in a second beam splitter for interference, and the other two photons are used as trigger signals. The two triggered photons are detected by two free running InGaAs avalanched single photon detectors (APD1, APD4, ID Quanta, ID220, 20% detection efficiency, 3 s dead time, dark count rate 4k cps), and the outputs of detectors APD1 and APD4 are used to trigger two single-photon detectors running in the gated mode (APD2, APD3, Qasky, Hefei, China, 100 MHz, free gating single photon detectors, 20% detection efficiency, dark count probability 410-5 per gate) for twophoton coincidence measurement. Detection output signals from APD2 and APD3 are sent to our coincidence count device (Pico quanta, TimeHarp 260, 1.6 ns coincidence window) for four-photon coincidence measurement. Before measuring the HOMI, we obtain a maximum-coincidence-to-accidental-coincidence ratio (CAR) of 131 by cooling the fiber in liquid nitrogen when the pump power is 23 W. There are a few remarks we want to point out.Firstly, the photon sources are not operated at the optimized pump pulse width for pure single photon generation, but narrow band 100 GHz filters are used in the experiments to increase the purity of the sources. Secondly, single photon detectors used in our experiment have lower detection efficiency and much higher dark counts than nano-wire single photon detectors, if we have high-performance nano-wire single photon detector, experimental results will be greatly improved due to the four-fold coincidences and dark coincidences scaling quadruplicate with the detection efficiency and dark count probability of a single detector. Thirdly, we use relatively high pump power for each DSF (0.12 mW) to reduce measurement time for photon coincidence, which will lead to a very poor raw visibility certainly. Finally, though only a 100 GHz channel pair is used in our experiment, we can use other channels for multiplexing such interference processes to improve the channel capacity in future quantum communication tasks theoretically. Our study shows greatly promising integrated optical elements for future scalable quantum information processing.