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Journal of the Optical Society of America B

Quantum entanglement of non-monochromatic photons on free electrons

Dmitry N. Makarov, K. A. Makarova, S. N. Kapustin, A. A. Goshev, Yu. V. Tsykareva

Published Nov 25, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.537983

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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.
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.
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.
In the present paper, an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schrödinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after interaction. The joint probability amplitudes are calculated for the detection of the electron at some space–time location and the detection of a definite number of photons. The analytical study of the time evolution of entanglement between the initially separated electron wave packet and the radiation mode leads to the conclusion that in general there are non-vanishing entropy remnants in the subsystems after the interaction. On the basis of the simple model to be presented here, the calculated values of the entropy remnants crucially depend on the character of the assumed switching-on and -off of the interaction.
Recent theories and experiments have explored the use of entangled photons as a spectroscopic probe of physical systems. We describe here a theoretical description for entropy production in the scattering of an entangled biphoton Fock state within an optical cavity. We develop this using perturbation theory by expanding the biphoton scattering matrix in terms of single-photon terms in which we introduce the photon-photon interaction via a complex coupling constant, ξ. We show that the von Neumann entropy provides a concise measure of this interaction. We then develop a microscopic model and show that in the limit of fast fluctuations, the entanglement entropy vanishes, whereas in the limit of slow fluctuations, the entanglement entropy depends on the magnitude of the fluctuations and reaches a maximum. Our result suggests that experiments measuring biphoton entanglement give microscopic information pertaining to exciton-exciton correlations.