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Europhysics Letters (EPL)

Schmidt expansion and quantum entanglement of non-monochromatic photons on free electrons

Dmitry N. Makarov, K. A. Makarova, A. A. Kharlamova

Published May 1, 2025• 0 citations
Publisher

Abstract

Abstract Recently it has been shown that quantum entanglement of photons is possible when they interact with free electrons. In reality, photons are not monochromatic and in many cases it is necessary to take into account the spectral width of such photons. In this paper, the Schmidt expansion for non-monochromatic photons interacting with free electrons is found. Their quantum entanglement is found based on the Schmidt parameter. It is shown that the degree of non-monochromaticity of photons greatly affects the result of quantum entanglement. As a result, the results obtained show that it is necessary to take into account the spectral width of incident photons. The limits of the spectral width of incident photons are established, when it can be neglected and photons can be considered monochromatic.

DOI
10.1209/0295-5075/add804

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Abstract Recently it has been shown that quantum entanglement of photons is possible when they interact with free electrons. In reality, photons are not monochromatic and in many cases it is necessary to take into account the spectral width of such photons. In this paper, the Schmidt expansion for non-monochromatic photons interacting with free electrons is found. Their quantum entanglement is found based on the Schmidt parameter. It is shown that the degree of non-monochromaticity of photons greatly affects the result of quantum entanglement. As a result, the results obtained show that it is necessary to take into account the spectral width of incident photons. The limits of the spectral width of incident photons are established, when it can be neglected and photons can be considered monochromatic.
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Abstract At present, the sources of entangled photons have a low rate of photon generation. This limitation is a key component of quantum informatics for the realization of such functions as linear quantum computation and quantum teleportation. In this paper, we propose a method for high intensity generation of entangled photons in a two‐mode electromagnetic field. On the basis of exact solutions of the Schrödinger equation, when electrons interact in an atom with a strong two‐mode electromagnetic field, it is shown that there may be large quantum entanglement between photons. The quantum entanglement is analyzed on the basis of the Schmidt parameter. It is shown that the Schmidt parameter can reach very high values depending on the choice of characteristics of the two‐mode fields. We find the Wigner function for the considered case. Violation of Bell's inequalities for continuous variables is demonstrated.
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.
The quantum entanglement of photons is one of the interesting and important manifestations of the quantum world, which is already being used in quantum technologies. The study of new methods of quantum entanglement of photons is one of the promising areas of quantum optics. In this work, it is shown that photons, in a two-mode electromagnetic field, can be quantum entangled when they interact with free electrons. It is shown that the quantum entanglement of such photons can be very large and such photons can be a good source of high quantum entanglement. In addition, it is shown that free electrons can be a beam splitter for a two-mode electromagnetic field.