On the Fast Electrons-Optical Modes Interaction Problem Error

Abstract:A recently developed relativistic quantum optics approach for a fast electron beam-optical modes interaction problem (Optica 6, 1524--1534 (2019)) contains suggestion about a smallness of the error induced by replacement $\Psi_{\vec k}\approx\Psi_{\vec k_0}$ for noninteracting free electron Dirac spinors at such wave vector $\vec k$ that $\left|\vec k-\vec k_0 \right| \ll\left|\vec k_0\right|$ with $\vec k_0$ as a peaked wave vector of a focused electron beam. Here, based on quantum information approach we strictly investigated a degree of coincidence of spinors $\Psi_{\vec k}$ and $\Psi_{\vec k_0}$ by calculating fidelity for them. The analytical expression is obtained. It is shown that the fidelity inevitably depends on not only wave vectors $\vec k$ and $\vec k_0$ but also on mutual orientation of $[\vec k_0,\vec k]$ and $\hat{\vec{s}}^{\dagger}\vec{\sigma}\hat{\vec{s}}$ with $\vec{s}$ is a two-component spin unit vector and $\vec{\sigma}$ is a vector of Pauli matrices. This result can be conceived as a chirality-like effect in the fidelity and constraints spin arbitrariness when applying the developed relativistic quantum optics approach to the problems of interest. A geometrical configuration of $\vec k_0$, $\vec k-\vec k_0$, and $\hat{\vec{s}}^†\vec\sigma\hat{\vec{s}}$ that is optimal in terms of fidelity is established.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2610.13976 [quant-ph]

(or arXiv:2610.13976v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.13976 Focus to learn more arXiv-issued DOI via DataCite

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