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Physics Letters A

Single-photon sources based on incomplete binary-tree multiplexers with optimized inputs

Петер Адам, Matyas I. Mechler

Published Mar 4, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1016/j.physleta.2024.129416

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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.
We consider novel types of spatially multiplexed single-photon sources based on output-extended incomplete binary-tree multiplexers containing general asymmetric routers where the construction of the multiplexers takes into account the total transmission efficiencies of the multiplexer arms at which a novel router can be added to the system. After selecting the multiplexer that outperforms the others, we identify the ranges of the loss parameters for which the application of the selected multiplexer leads to single-photon sources with higher single-photon probabilities and lower multiphoton noise than that can be achieved by using asymmetric multiplexers. We show that using the selected multiplexer is especially advantageous in the case of single-mode sources characterized by thermal statistics of the input photon pairs. We also reveal that the application of this multiplexer yields high performance single-photon sources even for suboptimal system sizes that is a typical situation in current experiments.
We propose two novel types of spatially multiplexed single-photon sources based on incomplete binary-tree multiplexers. The incomplete multiplexers are extensions of complete binary-tree multiplexers, and they contain incomplete branches either at the input or at the output of them. We analyze and optimize these systems realized with general asymmetric routers and photon-number-resolving detectors by applying a general statistical theory introduced previously that includes all relevant loss mechanisms. We show that the use of any of the two proposed multiplexing systems can lead to higher single-photon probabilities than that achieved with complete binary-tree multiplexers. Single-photon sources based on output-extended incomplete binary-tree multiplexers outperform those based on input-extended ones in the considered parameter ranges, and they can in principle yield single-photon probabilities higher than 0.93 when they are realized by state-of-the-art bulk optical elements. We show that the application of the incomplete binary-tree approach can significantly improve the performance of the multiplexed single-photon sources for suboptimal system sizes that is a typical situation in current experiments.
We propose two novel types of spatially multiplexed single-photon sources based on incomplete binary-tree multiplexers. The incomplete multiplexers are extensions of complete \nbinary-tree multiplexers, and they contain incomplete branches either at the input or at the output of them. We analyze and optimize these systems realized with general asymmetric routers and photon-number-resolving detectors by applying a general statistical theory introduced previously \nthat includes all relevant loss mechanisms. We show that the use of any of the two proposed multiplexing systems can lead to higher single-photon probabilities than that achieved with complete binary-tree multiplexers. Single-photon sources based on output-extended incomplete binary-tree multiplexers outperform those based on input-extended ones in the considered parameter ranges, and they can in principle yield single-photon probabilities higher than 0.93 \nwhen they are realized by state-of-the-art bulk optical elements. We show that the application of the incomplete binary-tree approach can significantly improve the performance of the multiplexed single-photon sources for suboptimal system sizes that is a typical situation in current experiments.
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 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.
We propose a scheme based on the multiplexing of heralded multiphoton sources for the generation of multiphoton Fock states. We theoretically analyze the performance of multiplexed multiphoton sources based on output-extended incomplete binary-tree multiplexers. We show that this system can be used to generate multiphoton states with considerably higher multiphoton probabilities than those that can be achieved with a single heralded multiphoton source. For multiplexed two-photon sources, we present detailed results on the optimization of the mean number of photon pairs generated in the heralded sources and the number of multiplexed units, which are relevant for the experimental realization.