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arXiv:1408.3266 · Physical Review A

Optimization of periodic single-photon sources

Петер Адам, Matyas I. Mechler, Imre Sánta, Mátyás Koniorczyk

Published Nov 18, 2014• 29 citations
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Abstract

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.

DOI
10.1103/physreva.90.053834

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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 consider periodic single-photon sources with combined multiplexing in which the outputs of several time-multiplexed sources are spatially multiplexed. We give a full statistical description of such systems in order to optimize them with respect to maximal single-photon probability. We carry out the optimization for a particular scenario which can be realized in bulk optics and its expected performance is extremely good at the present state of the art. We find that combined multiplexing outperforms purely spatially or time-multiplexed sources for certain parameters only, and we characterize these cases. Combined multiplexing can have the advantages of possibly using less nonlinear sources, achieving higher repetition rates, and the potential applicability for continuous pumping. We estimate an achievable single-photon probability between 85% and 89%.
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.
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.
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 propose a spatially multiplexed single-photon source where the structure of the applied binary-tree multiplexer is optimized systematically during its construction. Along the building procedure of this type of multiplexer, the position of a binary photon router appended to the tree in a step of the expansion is determined by taking into account the current achievable single-photon probability of the source. The method chooses the position where this probability is maximal. We determine the stepwise optimized binary-tree multiplexers for experimentally realizable values of the loss parameters, and for a fixed number of routers. The method is scalable, that is, it is possible to determine the multiplexer with an optimal structure for any number of photon routers. We show that single-photon sources based on stepwise optimized binary-tree multiplexers yield higher single-photon probabilities than single-photon sources based on any spatial multiplexer types discussed in the literature thus far in the considered ranges of the loss parameters.
We develop a method for optimizing the structure of general binary-tree multiplexers realized with asymmetric photon routers aiming at improving the performance of spatially multiplexed single-photon sources. Our procedure systematically considers all possible binary-tree multiplexers that can be constructed using a certain number of photon routers. Using this method one can select the multiplexer structure that leads to the highest single-photon probability for a given set of loss parameters characterizing the system. We determine the optimal general binary-tree multiplexers for experimentally realizable values of the transmission coefficients of the photon routers and that of the detector efficiency. We show that single-photon sources based on such optimal multiplexers yield higher single-photon probabilities than what can be achieved with single-photon sources based on any other spatial multiplexer considered in the literature. Our approach improves the performance of multiplexed single-photon sources even for small system sizes which is the typical situation in current experiments.