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Entropy

Quantum Entanglement of Monochromatic and Non-Monochromatic Photons on a Waveguide Beam Splitter

Dmitry N. Makarov, Yu. V. Tsykareva

Published Dec 27, 2021• 6 citations
Publisher

Abstract

It is well known that the waveguide beam splitter can be used as a source for the quantum entanglement of photons. The analysis of such quantum entanglement is a difficult problem even for monochromatic photons, since the system under study is multiparametric. This paper will show that quantum entanglement can be represented in a simple form not only for monochromatic photons but also for non-monochromatic ones. It will be shown that quantum entanglement for non-monochromatic photons can be very different from monochromatic photons, which can be used to create large quantum entanglement.

DOI
10.3390/e24010049

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It is well known that the waveguide beam splitter can be used as a source for the quantum entanglement of photons. The analysis of such quantum entanglement is a difficult problem even for monochromatic photons, since the system under study is multiparametric. This paper will show that quantum entanglement can be represented in a simple form not only for monochromatic photons but also for non-monochromatic ones. It will be shown that quantum entanglement for non-monochromatic photons can be very different from monochromatic photons, which can be used to create large quantum entanglement.
It is well known that a beam splitter (BS) can be used as a source of photon quantum entanglement. This is due to the fact that the statistics of photons changes at the output ports of the BS. Usually, quantum entanglement and photon statistics take into account the constancy of the reflection coefficient R or the transmission coefficient T of the BS, where [Formula: see text]. It has recently been shown that if BS is used in the form of coupled waveguides, the coefficients R and T will depend on the photon frequencies. In this paper, it is shown that the quantum entanglement and statistics of photons at the output ports of a BS can change significantly if a BS is used in the form of coupled waveguides, where the coefficients R and T are frequency-dependent.
Studying beam splitters as sources of entangled photons is a relevant topic in modern physics. In most cases, in quantum optics the theories of waveguide beam splitters of large and small sizes have no difference. In this work, it is shown that a nanosized waveguide beam splitter has a significant difference from a similar device, but on a larger scale. The output wave function of the beam splitter’s ports is analyzed in the arbitrary case of photons entering the first and second ports. The results obtained are sensitive to the size of the waveguide beam splitter, the coupling parameter of two waveguides, the monochromatic photons case of a linear beam splitter and the non-monochromaticity grade for photons entering both input ports of the beam splitter. The results are very important for various quantum technologies (e.g. integrated circuits, optical quantum computers) which use this type of beam splitter and quantum metrology.
Relatively recently, it became known that the interaction of photons with free electrons leads to quantum entanglement of photons. Such photons can be used in many applications of quantum technologies. Typically, to study quantum entanglement, photons are assumed to be monochromatic, although in reality they are not. This paper shows that if non-monochromatic photons are taken into account, their quantum entanglement, based on von Neumann entropy, can differ significantly from the case of monochromatic photons. It has been shown that the entanglement of non-monochromatic photons can be large and reach the maximum possible value.
Usually in quantum optics, the theory of large- and small-scale waveguide beam splitters is the same. In this paper, it is shown that the theory of the nanoscale waveguide beamsplitter has a significant difference from a similar device, but of a larger scale. It is shown that the previously known theory of the waveguide beam splitter is a particular case of the theory presented here. The wave function at the output ports of the nanoscale beam splitter is analyzed. The results obtained are sensitive to the size of the beam splitter, the coupling parameter of the two waveguides, and the degree of nonmonochromaticity of the photons entering the first and second ports of the beam splitter. The results are important for quantum technologies using a nanosized beam splitter.
The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients R (or the transmission coefficient T, where R+T=1) and the phase shift ϕ. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where R and ϕ depend in a special way on photon frequencies. Based on this, this review systematizes the concept of BS in quantum optics into “Conventional” and frequency-dependent BS, and also presents the theory of such BS. It is shown that the quantum entanglement, photon statistics at the output ports, and the Hong–Ou–Mandel (HOM) effect for such BS can be very different. Taking into account the fact that the waveguide BS is currently acquiring an important role in quantum technologies due to the possibility of its miniaturization, this review will be useful not only for theoreticians, but also for experimenters.