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Applied Optics

Modeling the avalanche diode as a photon detector in quantum optical interferometers

Kay Schmid, Erna M. Frins, Wolfgang Dultz, Heidrun Schmitzer

Published Oct 23, 2012• 1 citation
Publisher

Abstract

Avalanche diodes (ADs) are widely used to count photons in quantum interferometry. In reality they do not count photons, but click once when a bunch of photons arrives in a light pulse. We model this behavior in typical quantum optical interferometers like the Hong-Ou-Mandel beam splitter and the Mach-Zehnder interferometer, and compare it with the behavior of the photon-number-resolving (PNR) detector and the Hanbury-Brown-Twiss detector in these measuring devices. Our results show that quantum interferometric measurements with biphotons could be performed with single ADs, if the noise of the diodes could be reduced. Even a single PNR detector can be used in these interferometers, if the variance of the measurement is determined, since it reveals information about biphoton interference in contrast to the single detector counting rate.

DOI
10.1364/ao.51.007560

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Avalanche diodes (ADs) are widely used to count photons in quantum interferometry. In reality they do not count photons, but click once when a bunch of photons arrives in a light pulse. We model this behavior in typical quantum optical interferometers like the Hong-Ou-Mandel beam splitter and the Mach-Zehnder interferometer, and compare it with the behavior of the photon-number-resolving (PNR) detector and the Hanbury-Brown-Twiss detector in these measuring devices. Our results show that quantum interferometric measurements with biphotons could be performed with single ADs, if the noise of the diodes could be reduced. Even a single PNR detector can be used in these interferometers, if the variance of the measurement is determined, since it reveals information about biphoton interference in contrast to the single detector counting rate.
Quantum-light sources based on semiconductor quantum dots (QDs) are promising candidates for many applications in quantum photonics and quantum communication. Important emission characteristics of such emitters, namely the single-photon purity and photon indistinguishability, are usually assessed via time-correlated measurements using standard 'click' detectors in Hanbury Brown and Twiss or Hong-Ou-Mandel (HOM-) type configurations. In this work, we employ a state-of-the-art photon-number-resolving (PNR) detection system based on superconducting transition-edge sensors (TESs) to directly access the photon-number distribution of deterministically fabricated solid-state single-photon sources. Offering quantum efficiencies close to unity and high energy resolution, our TES-based two-channel detector system allows us to analyse the quantum optical properties of a QD-based non-classical light source. In particular, it enables the direct observation of the two-particle Fock-state resulting from interference of quantum mechanically indistinguishable photons in HOM-experiments. Additionally, comparative measurements reveal excellent quantitative agreement of the photon-indistinguishabilities obtained with PNR ((90 ± 7)%) and standard click ((90 ± 5)%) detectors. Our work thus demonstrates that TES-based detectors are perfectly suitable for the quantum metrology of non-classical light sources and higlights appealing prospects for the efficient implementation of quantum information tasks based on multi-photon states.
When a photon interferes with itself while traversing a Mach-Zehnder interferometer, the output port where it emerges is influenced by the phase difference between the interferometer arms. This allows for highly precise estimation of the path length difference (delay) but is extremely sensitive to phase noise. By contrast, a delay between the arms of the two-photon Hong-Ou-Mandel interferometer directly affects the relative indistinguishability of the photon pair, affecting the rate of recorded coincidences. This likewise allows for delay estimation, notably less precise but with the advantage of being less sensitive to perturbations of the photons' phase. Focusing on two-photon input states, we here investigate to what degree of noise Mach-Zehnder interferometry retains its edge over Hong-Ou-Mandel interferometry. We also explore the competing benefits of different two-photon inputs for a Mach-Zehnder interferometer and under what parameter regimes each input performs best.
Multiphoton interference effects can be measured with a single detector when two input photons are temporally well separated when compared with the dead time of the single-photon avalanche detector. Here we experimentally demonstrate that the Hong-Ou-Mandel interference effect can be observed with a single non-photon-number resolving detector via a time-delayed coincidence measurement of successive electrical signals from the detector. The two-photon interference experiment is performed by utilizing temporally well-separated pairwise weak coherent pulses, and the interference fringes are successfully measured with high visibility in the range of the limited upper bound for the weak coherent photon source.
Single-photon sources are at the heart of quantum-optical networks, with their uniquely quantum emission and phenomenon of two-photon interference allowing for the generation and transfer of nonclassical states. Although a few analytical methods have been briefly investigated for describing pulsed single-photon sources, these methods apply only to either perfectly ideal or at least extremely idealized sources. Here, we present the first complete picture of pulsed single-photon sources by elaborating how to numerically and fully characterize non-ideal single-photon sources operating in a pulsed regime. In order to achieve this result, we make the connection between quantum Monte-Carlo simulations, experimental characterizations, and an extended form of the quantum regression theorem. We elaborate on how an ideal pulsed single-photon source is connected to its photocount distribution and its measured degree of second- and first-order optical coherence. By doing so, we provide a description of the relationship between instantaneous source correlations and the typical experimental interferometers (Hanbury-Brown and Twiss, Hong–Ou–Mandel, and Mach–Zehnder) used to characterize such sources. Then, we use these techniques to explore several prototypical quantum systems and their non-ideal behaviors. As an example numerical result, we show that for the most popular single-photon source—a resonantly excited two-level system—its error probability is directly related to its excitation pulse length. We believe that the intuition gained from these representative systems and characters can be used to interpret future results with more complicated source Hamiltonians and behaviors. Finally, we have thoroughly documented our simulation methods with contributions to the Quantum Optics Toolbox in Python in order to make our work easily accessible to other scientists and engineers.
A technique for the simulation of multimode quantum optical interferometry and protocols in quantum communications is introduced. This technique is very efficient at simulating in the single-photon-counting regime. This works by treating the photons in the system as members of a multiphoton pulse and reducing the computation of measurable quantities to overlap integrals that may be precomputed and combined in a recursive algorithm. The simulation of a Mach-Zehnder interferometer and the Hong-Ou-Mandel effect are demonstrated using this technique. The results of these simulations perfectly agree with the theoretical results. Additionally, since the effects of the components in the system can be integrated into the quantum operators involved, the technique is agnostic to the components introduced into the system.
Single-photon detectors are a pivotal component in photonic quantum technologies. A precise and comprehensive calibration of the inherent detection efficiency is of utmost importance to ensure the proper evaluation of the performance in view of the specific technological application of interest, such as the protection against security breaches in quantum cryptographic solutions. Here we report on a systematic study and comprehensive analysis of the estimation of the inherent detection efficiency of two commercial single-photon detectors based on single-photon avalanche diodes for various mean photon numbers and at high laser pulse repetition rates using different techniques. We observe an unexpected and significant drop in the inherent detection efficiency at detection rates of 10% and higher relative to the maximum detection rate. It is demonstrated that for data analysis a statistical model for the detection rate conveniently can be used if no time-stamped data are available. We conclude that the full characterization of single-photon detectors used in critical applications should include the sensitivity of their inherent detection efficiency to high event rates.