Photon number conservation and photon interference

The group theoretical aspect of the description of passive lossless optical four-ports (beam splitters) is revisited. It is shown through an example, that this approach can be useful in understanding interferometric schemes where a low number of photons interfere. The formalism is extended to passive lossless optical six-ports, their SU(3)-theory is outlined.Comment: Contribution at "Classical and Quantum Interference" workshop in RCO, Olomouc, Oct. 25-26 2001. A corrected versio

Optimization of periodic single-photon sources based on combined multiplexing

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 potentially the best 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%.Comment: 11 pages, 6 figur

Optimization of periodic single-photon sources

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 novel 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.Comment: 13 pages, 18 figure

Single-photon sources based on asymmetric spatial multiplexing with optimized inputs

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

The Column Generatiion and Traiin Crew Scheduliing

Better productivity and efficiency is more and more required in the railway operation. The train crew management is one of the several problems that could be solved using mathematical methods. Crew management is a problem that is well-known in Operations Research. We compare two approaches for solving the train crew scheduling problem. The first approach consists of solving the original problem by single model. The second approach corresponds to the step-by-step column generation. This technique was originally based on Dantzig-Wolfe decomposition. The benchmarks used for comparison of both approaches originate in real problems from railway systems in Slovakia and Hungary

Preconditioning in the Backtracking Duty Generation of Passenger Rail Crew Scheduling: A Case Study

We describe briefly the crew scheduling and rostering approach implemented in Railm@n, the system used by MAV START, the passenger railway transport company of Hungary, to organize the work of passenger train crews that is, conductors. Then we discuss the scheduling (duty generation) phase of the algorithm in detail. When treated in full generality, the problem already scales to an untractable size. We describe our successful experience with the use of preconditioning to keep the problem tractable. The approach may be useful in timetable planning and depot planning, too