Non-diffracting multi-electron vortex beams balancing their electron–electron interactions

Abstract

The wave-like nature of electrons has been known for almost a century, but only in recent years has the ability to shape the wavefunction of EBeams (Electron-Beams) become experimentally accessible. Various EBeam wavefunctions have been demonstrated, such as vortex, self-accelerating, Bessel EBeams etc. However, none has attempted to manipulate multi-electron beams, because the repulsion between electrons rapidly alters the beam shape. Here, we show how interference effects of the quantum wavefunction describing multiple electrons can be used to exactly balance both the repulsion and diffraction-broadening. We propose non-diffracting wavepackets of multiple electrons, which can also carry orbital angular momentum. Such wavefunction shaping facilitates the use of multi-electron beams in electron microscopy with higher current without compromising on spatial resolution. Simulating the quantum evolution in three-dimensions and time, we show that imprinting such wavefunctions on electron pulses leads to shape-preserving multi-electrons ultrashort pulses. Our scheme applies to any beams of charged particles, such as protons and ion beams.

Theory and applications of free-electron vortex states

“…Such accurate description of interacting electrons and fields remains a challenge. Recently, this problem was analysed using a Hartree-Fock approach in [188], where non-diffracting vortexbeam solutions with balanced electron-electron interaction were found.…”

Relativistic free electrons based quantum physics

“…Kaminer等 [93] 从理论上提 出了利用Q-PINEM产生猫态以及在连续变量的 量子计算和通信中起着关键作用的GKP态的方 法, 该方法能够在10%的后选择概率下生成超过 10 dB压缩和90%以上保真度的光学GKP态. 缠 [107,108] . 两个空间分离的光子态可以通过各种系 统实现, 如光子晶体腔、硅光子波导等, 因此这种 概念可以很容易地被拓展到其他PQs系统中, 如 图 17 利用Q-PINEM塑造具有新奇量子统计的光子态 [38] (a) Q-PINEM相互作用的物理实现示意图; (b) 单次Q-PINEM相 互作用的方案 Fig.…”

Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum

“…The wave-like behavior of electrons can be described as a complex-value wave function whose degrees of freedom corresponding to the radial and azimuthal indices determine their spatial structure . By controlling these parameters and leveraging recent advances in nanofabrication and electron microscopy techniques, remarkable progress has been realized toward generating structured electron beams with tailored wave packets including the electron vortex beam (EVB), − electron Hermite–Gaussian beam, , electron Airy beam, , and electron Bessel beam. − Particularly, the generation of EVBs in free space has garnered considerable attention owing to their potential to extend the functionalities of electron microscopy …”