论文标题
涡流电子电磁辐射中的非线性量子效应
Non-linear quantum effects in electromagnetic radiation of a vortex electron
论文作者
论文摘要
关于如何与光与物质的空间相干性解释电子的相互作用存在争议。当这样的电子散发光子时，它可以做到，好像它的电荷被限制在连贯长度内的一个点，即波函数的正方形模量$ |ψ|^2 $的区域是本地化的，或者作为连续的空间电荷云扩散在其上。在最近的一项研究中解决了这个问题。莱特牧师。 {\ bf 123}，060401（2019），得出结论以支持第一个（点）解释。在这里，我们认为该论文中报告的测量值有另一种解释，该解释依赖于纯粹的经典论点，并且不允许人们反驳第二种解释。我们提出了一个来自携带轨道角动量的非相关涡流电子的史密斯 - 纯辐射实验，这可以明确地导致相反的结论。除了近似近似之外，涡流包具有非点电动四极矩，随着数据包的传播而增长并导致辐射强度的非线性$ l^3 $增长，当$ L $的长度$ l $时，$ L $的长度比包装的rayleigh的长度大得多。对于单电子，从未观察到这种非线性效应，如果检测到，它将是波数据包中电荷性质的标志。因此，$ |ψ|^2 $的两个视图相互互补，电子辐射为点电荷，或者是连续电荷流，具体取决于实验条件和量子状态。我们的结论适用于大型的非高斯数据包和发射过程，其辐射形成长度可以超过瑞利长度，例如Cherenkov辐射，过渡辐射，衍射辐射等。
There is a controversy of how to interpret interactions of electrons with a large spatial coherence with light and matter. When such an electron emits a photon, it can do so either as if its charge were confined to a point within a coherence length, the region where a square modulus of a wave function $|ψ|^2$ is localized, or as a continuous cloud of space charge spread over it. This problem was addressed in a recent study R.~Remez, et al., Phys. Rev. Lett. {\bf 123}, 060401 (2019) where a conclusion was drawn in favor of the first (point) interpretation. Here we argue that there is an alternative explanation for the measurements reported in that paper, which relies on purely classical arguments and does not allow one to refute the second interpretation. We propose an experiment of Smith-Purcell radiation from a non-relativistic vortex electron carrying orbital angular momentum, which can unambiguously lead to the opposite conclusion. Beyond the paraxial approximation, the vortex packet has a non-point electric quadrupole moment, which grows as the packet spreads and results in a non-linear $L^3$-growth of the radiation intensity with the length $L$ of the grating when $L$ is much larger than the packet's Rayleigh length. Such a non-linear effect has never been observed for single electrons and, if detected, it would be a hallmark of the non-point nature of charge in a wave packet. Thus, two views on $|ψ|^2$ are complementary to each other and an electron radiates either as a point charge or as a continuous charge flow depending on the experimental conditions and on its quantum state. Our conclusions hold for a large class of non-Gaussian packets and emission processes for which the radiation formation length can exceed the Rayleigh length, such as Cherenkov radiation, transition radiation, diffraction radiation, and so forth.
