4(a) and from statistics in the case of monochromatic photons at maximum quantum entanglement, i.e. This statistic differs from the statistic of the HOM effect Fig. It is quite interesting to see the statistics of photons at maximum quantum entanglement, see Fig.
By increasing \(\sigma / \Omega\) the HOM effect disappears and the photon statistics changes dramatically. This means that only pairs of photons are recorded on the first or second detectors (in the figure, this is for \(k = 0\) and \(k = 2\)) with a probability of 1/2.
4(a) you can see that for the states \(| 1,1 \rangle\) at \(\sigma / \Omega = 0\) the HOM effect 2 is realized. It is shown that even in the case of completely identical photons and a balanced BS in the HOM effect, the visibility \(\mathcal \)), but not monochromatic photons.The calculation results are presented in Fig. In addition, this change affects a fundamental understanding of the HOM effect itself. For example, in the works 18, 19 it was shown that the well-known theory of Hong-Ou-Mandel (HOM) interference, based on the constancy of the coefficients \(R = 1/2\) and \(T = 1/2\), can be significantly changed. This dependence can be significant and must be taken into account in many applications of quantum optics. In this work, it was shown that if the BS is presented in the form of coupled waveguides, then the coefficients R and T depend on the frequencies of the photons entering both ports of the BS. Recently, the paper 17 presented the theory of a frequency-dependent BS in the form of coupled waveguides. Coupled waveguide BS has an advantage over prismatic because it is much smaller than prismatic BS and also has many other advantages 3, 9, 13.Ĭurrently, theories describing quantum entanglement and statistics of photons at the BS output ports are based on the constancy of the main parameters of the BS: the reflection coefficient R and the transmission coefficient T, where \(R + T = 1\) see e.g. Coupling between waveguides can be achieved when two waveguides are brought together close enough to each other so that the electromagnetic fields overlap in this case it is a directional coupler (for example 11, 12). An analogue of a prismatic BS can be a BS in the form of coupled waveguides. Therefore, they are most often used in experiments, but not in quantum technologies. The prismatic BS has a drawback that is its size. The most common and well-known type is the prismatic BS. Beam splitters currently can be of various types. showed that using BS, phase shifters, photodetectors and single photon sources, it is possible to create a universal quantum computer (KLM protocol) 10. Quantum entanglement and changes in the statistics of photons in BS can be used in linear optical quantum computing (LOQC) 7, 8, 9. At the same time, quantum entanglement is the basis in new directions of quantum optics: quantum metrology 5, quantum information 6, etc. It is well known that a beam splitter (BS) is a source of quantum entangled photons 1, 2, 3, 4.