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Optics Express

Coincidence detection theory for time-correlated photon sources

Zijun Chen, Yeshaiahu Fainman

Published Nov 6, 2024• 2 citations
Publisher

Abstract

This work presents a probability theory of coincidence detection to address the detection limit of time-correlated photon sources. We use Bayes’ theorem to model instruments as a noisy communication channel and apply statistical inference to identify the minimum detectable coincidence rate. Photon triplet generation is considered as a case study to illustrate the application of coincidence detection theory for time-correlated photon sources that are based on spontaneous parametric down-conversion. A triplet generation rate of 1–100 Hz is required for source characterization performed over 1–72 hours using superconducting nanowire single-photon detectors. We envision the connection between Bayes’ theorem and coincidence detection opens up a new avenue for applying signal processing techniques available in information theory to photon coincidence measurements.

DOI
10.1364/oe.538831

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This work presents a probability theory of coincidence detection to address the detection limit of time-correlated photon sources. We use Bayes’ theorem to model instruments as a noisy communication channel and apply statistical inference to identify the minimum detectable coincidence rate. Photon triplet generation is considered as a case study to illustrate the application of coincidence detection theory for time-correlated photon sources that are based on spontaneous parametric down-conversion. A triplet generation rate of 1–100 Hz is required for source characterization performed over 1–72 hours using superconducting nanowire single-photon detectors. We envision the connection between Bayes’ theorem and coincidence detection opens up a new avenue for applying signal processing techniques available in information theory to photon coincidence measurements.
Photon triplet generation based on third-order spontaneous parametric down-conversion remains as an experimental challenge. The challenge stems from the trade-offs between source brightness and instrument noise. This work presents a probability theory of coincidence detection to address the detection limit in source characterization. We use Bayes' theorem to model instruments as a noisy communication channel and apply statistical inference to identify the minimum detectable coincidence rate. A triplet generation rate of 1-100 Hz is required for source characterization performed over 1-72 hours using superconducting nanowire single-photon detectors.
Photon correlated beams, generated by parametric down-conversion in nonlinear crystals (PDC), have been proved successfully for the measurement of quantum efficiency, of single photon detectors [1, 2, 3, 4] and can be used for measuring transmittance, as well. The main feature relies on the realization of two correlated quantum channels yielding coincident events. To reduce uncertainty [4, 5, 6] and determine its ultimate limit, contributions to statistical noise in a real experimental set-up are here investigated, and a general model is proposed to calculate the maximum likelihood best estimators and evaluate the probability of coincidence. In typical measurement scheme a channel is set as trigger (idler, i) and attention is paid to catch at least the same amount of correlated photons in the other channel (signal, s) [4]. Unwanted uncorrelated photons due to PDC itself result in a decreased degree of correlation, noise fluctuations in coincidence measurements and asymmetry between the two channels, whose mean photon rate can be quite different. We indicate by with the mean rate of correlated photons in s and i channels We address the total mean photon rates in both channels as where terms take into account also additive background photon rates due to straylight and detector noise. Actually statistical noise is also due to losses of correlated photons by optical elements, non ideal detectors and electronic devices in both channels. We distinguish, therefore, between optical losses ( transmittance of the correlated photon path), detection losses detectorquantum efficiency), electronic losses associated to the dead times time during which the detection system is unable to detect photons). It is usual to identify dead times as non-extending and extending: in the first case, all photons following a revealed photon within the fixed time interval are ignored, while in the second case any incoming photon produces or prolongs Eventually the finite duration of the time coincidence window, modifies the distribution probability of coincident events. Let us consider the distribution probability of single channel
This study discusses the correction factors in detection efficiency measurements based on spontaneous parametric down-conversion (SPDC) and coincidence counting. To address the coincidence loss induced by relative delays between two detection channels, this study proposes an accurate calculation analysis based on counting probability statistics derived from coincidence events. Additionally, an approximate method utilizing histograms and the photon count rate of detectors is proposed, which can effectively reduce the errors in coincidence loss corrections. Furthermore, the study discusses the dead time of single-photon detectors (SPDs) and proposes a weighted-average method applicable for correcting the influence of dead time.
We present a full triple-coincidence analysis of photon-pair states generated by spontaneous parametric down-conversion. By increasing the coherence time of the source with the help of an intracavity setup, our measurements are not spoiled by detection time jitter. Signal-idler, but also thermal signal-signal, correlations are clearly resolved in this regime. Via introduction of an artificial coincidence window, we discuss in detail the transition to the previously studied cases where typically no single-arm correlation is observed. We investigate the heralded antibunching characteristics to show that in our system further studies of continuously generated photon states, possibly higher-photon-number entangled states, can be performed with respect to their (non)applicability in quantum information tasks.
We analyze the generation rates and preparation fidelities of photon triplet states in pulsed cascaded parametric down-conversion (PDC) under realistic experimental circumstances. As a model system, we assume a monolithically integrated device with negligible interface loss between the two consecutive PDC stages. We model the secondary down-conversion process in terms of a lossy channel and provide a detailed analysis of noise contributions. Taking variable pump powers into account, we estimate the impact of higher-order photon contributions and conversion processes on the achievable coincidence probabilities. At mean photon numbers of ⟨m⟩∼0.25\langle m\rangle\sim0.25⟨m⟩∼0.25 photons per pulse behind the first PDC stage, we expect around 4.04.04.0 genuine photon triplets per hour. Additionally, we discuss fundamental limitations of our model system as well as feasible improvements to the detectable photon triplet rate.
Heralded single-photon sources are the most commonly used sources for optical quantum technology applications. There is strong demand for accurate prediction of their spectral features and temporal correlations with ever-increasing precision. This is particularly important in connection with the intrinsically stochastic photon-pair generation process in heralded sources. Here we present a complete theoretical description of the temporal correlation of a signal-idler, signal-signal, and signal-signal-idler coincidences of photons generated by continuous-wave pumped cavity-enhanced spontaneous parametric down-conversion. The theory excellently predicts the measurements, which has been experimentally confirmed in our setup utilizing single-photon detectors with high temporal resolution. This enables us to resolve and analyze the multiphoton correlation functions in great detail.