Spatially multiplexed single-photon sources based on binary-tree multiplexers with optimized structure

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.