Single-photon sources based on stepwise optimized binary-tree multiplexers

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.