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Photonics

Reducing Multiphoton Noise in Multiplexed Single-Photon Sources

Петер Адам, Matyas I. Mechler

Published Aug 4, 2024• 2 citations
Publisher

Abstract

Multiplexed single-photon sources can produce indistinguishable single photons with high probability in near-perfect spatial modes. Such systems, realized with optical elements having losses, can be optimized—that is, both the optimal number of multiplexed units in the sources and the optimal mean number of photon pairs generated in a multiplexed unit, for which the output single-photon probability is maximal, can be determined. The accompanying multiphoton noise of the sources, arising from the probabilistic nature of the underlying physical processes in these systems, can be detrimental in certain applications. Inspired by this fact, we develop a procedure aimed at decreasing the multiphoton noise of multiplexed single-photon sources. The procedure is based on the reoptimization of the system for the chosen value of the normalized second-order autocorrelation function characterizing the multiphoton noise. The results of this reoptimization are shown for two types of spatially multiplexed single-photon sources. We find that by applying the proposed procedure, the multiphoton noise can be considerably decreased along with a relatively low decrease in the single-photon probability. Although the method presented here is for two spatially multiplexed single-photon sources, it can be applied straightforwardly for any type of multiplexed single-photon source.

DOI
10.3390/photonics11080728

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Multiplexed single-photon sources can produce indistinguishable single photons with high probability in near-perfect spatial modes. Such systems, realized with optical elements having losses, can be optimized—that is, both the optimal number of multiplexed units in the sources and the optimal mean number of photon pairs generated in a multiplexed unit, for which the output single-photon probability is maximal, can be determined. The accompanying multiphoton noise of the sources, arising from the probabilistic nature of the underlying physical processes in these systems, can be detrimental in certain applications. Inspired by this fact, we develop a procedure aimed at decreasing the multiphoton noise of multiplexed single-photon sources. The procedure is based on the reoptimization of the system for the chosen value of the normalized second-order autocorrelation function characterizing the multiphoton noise. The results of this reoptimization are shown for two types of spatially multiplexed single-photon sources. We find that by applying the proposed procedure, the multiphoton noise can be considerably decreased along with a relatively low decrease in the single-photon probability. Although the method presented here is for two spatially multiplexed single-photon sources, it can be applied straightforwardly for any type of multiplexed single-photon source.
We introduce a theoretical framework which is suitable for the description of all spatial and time-multiplexed periodic single-photon sources realized or proposed thus far. Our model takes into account all possibly relevant loss mechanisms. This statistical analysis of the known schemes shows that multiplexing systems can be optimized in order to produce maximal single-photon probability for various sets of loss parameters by the appropriate choice of the number of multiplexed units of spatial multiplexers or multiplexed time intervals and the input mean photon pair number and reveals the physical reasons of the existence of the optimum. We propose a time-multiplexed scheme to be realized in bulk optics, which, according to the present analysis, would have promising performance when experimentally realized. It could provide a single-photon probability of 85% with a choice of experimental parameters which are feasible according to the experiments known from the literature.
We develop a statistical theory describing the operation of multiplexed single-photon sources equipped with photon-number-resolving detectors that includes the potential use of different input mean photon numbers in each of the multiplexed units. This theory accounts for all relevant loss mechanisms and allows for the maximization of the single-photon probabilities under realistic conditions by optimizing the different input mean photon numbers unit-wise and the detection strategy that can be defined in terms of actual detected photon numbers. We apply this description to analyze periodic single-photon sources based on asymmetric spatial multiplexing realized with general asymmetric routers. We show that optimizing the different input mean photon numbers results in maximal single-photon probabilities higher than those achieved by using optimal identical input mean photon numbers in this setup. We identify the parameter ranges of the system for which the enhancement in the single-photon probability for the various detection strategies is relevant. An additional advantage of the unit-wise optimization of the input mean photon numbers is that it can result in the decrease of the optimal system size needed to maximize the single-photon probability. We find that the highest single-photon probability that our scheme can achieve in principle when realized with state-of-the-art bulk optical elements is 0.935. This is the highest one to our knowledge that has been reported thus far in the literature for experimentally realizable single-photon sources.
We analyze single-photon sources based on minimum-based, maximum-logic output-extended incomplete binary-tree multiplexers assuming different input mean photon numbers in each of the multiplexed units. This approach results in maximal single-photon probabilities higher than those achieved with optimal identical input mean photon numbers. The proposed technique decreases the multiphoton noise of the sources and it is especially advantageous for lower detector efficiencies. We show that assuming different input mean photon numbers in the multiplexed units, single-photon sources based on the analyzed multiplexers outperform those based on asymmetric multiplexers for the major part of the considered parameter range.
Detectors inherently capable of resolving photon numbers have undergone a significant development recently, and this is expected to affect multiplexed periodic single-photon sources where such detectors can find their applications. We analyze various spatially and time-multiplexed periodic single-photon source arrangements with photon-number-resolving detectors, partly to identify the cases when they outperform those with threshold detectors. We develop a full statistical description of these arrangements in order to optimize such systems with respect to maximal single-photon probability, taking into account all relevant loss mechanisms. The model is suitable for the description of all spatial and time multiplexing schemes. Our detailed analysis of symmetric spatial multiplexing identifies a particular range of loss parameters in which the use of the new type of detectors leads to an improvement. Photon number resolution opens an additional possibility for optimizing the system in that the heralding strategy can be defined in terms of actual detected photon numbers. Our results show that this kind of optimization opens an additional parameter range of improved efficiency. Moreover, this higher efficiency can be achieved by using less multiplexed units, i.e., smaller system size as compared to threshold-detector schemes. We also extend our investigation to certain time-multiplexed schemes of actual experimental relevance. We find that the highest single-photon probability is 0.907 that can be achieved by binary bulk time multiplexers using photon-number-resolving detectors.
An on-demand single-photon source is a key requirement for scaling many optical quantum technologies. A promising approach to realize an on-demand single-photon source is to multiplex an array of heralded single-photon sources using an active optical switching network. However, the performance of multiplexed sources is degraded by photon loss in the optical components and the non-unit detection efficiency of the heralding detectors. We provide a theoretical description of a general multiplexed single-photon source with lossy components and derive expressions for the output probabilities of single-photon emission and multi-photon contamination. We apply these expressions to three specific multiplexing source architectures and consider their tradeoffs in design and performance. To assess the effect of lossy components on near- and long-term experimental goals, we simulate the multiplexed sources when used for many-photon state generation under various amounts of component loss. We find that with a multiplexed source composed of switches with ∼ 0.2 − 0.4 dB loss and high efficiency number-resolving detectors, a single-photon source capable of efficiently producing 20–40 photon states with low multi-photon contamination is possible, offering the possibility of unlocking new classes of experiments and technologies.
The properties of a heralded single-photon source with temporal and spatial multiplexing are studied with the aim to maximize its efficiency for a given value of the second-order zero-time autocorrelation function. We show that the variable time delay, which is used for temporal multiplexing, can be optimized so that the mean number of photon passes through the switches and the total number of switches are respectively reduced to ∼ log 2 N and ∼ (1/2)log 2 N , where N is the temporal multiplexing degree. The total efficiency of such an optimized source is calculated for typical switching losses and the autocorrelation function is calculated in the presence of the detector dark-count noise.