[Paper Review] Coulomb interactions and the spatial coherence of femtosecond nanometric electron pulses

Stefan Meier, Peter Hommelhoff|arXiv (Cornell University)|Dec 23, 2021

Advanced Electron Microscopy Techniques and Applications41 references16 citations

TL;DR

This study experimentally demonstrates that Coulomb interactions reduce the spatial coherence of femtosecond electron pulses from laser-triggered tungsten needle tips, even at sub-one-electron average charge per pulse. Using electron interference fringes and the van Cittert-Zernike theorem, the authors quantitatively link visibility loss to an effective source size increase, showing a 35% drop in visibility (to 65% of baseline) at just 1.4 electrons per pulse due to electron-electron repulsion.

ABSTRACT

The transverse coherence of electrons is of utmost importance in high resolution electron microscopes, point-projection microscopes, low-energy electron microscopy and various other applications. Pulsed versions of many of these have recently been realized, mostly relying on femtosecond laser-triggering electron emission from a sharp needle source. We here observe electron interference fringes and measure how the interference visibility becomes reduced as we increase the electron bunch charge. Due to the extremely strong spatio-temporal confinement of the electrons generated here, we observe the visibility reduction already at average electron bunch charges of less than 1 electron per pulse, owing to the stochastic nature of the emission process. We can fully and quantitatively explain the loss of coherence based on model simulations. Via the van Cittert-Zernike theorem we can connect the visibility reduction to an increase of the effective source size. We conclude by discussing emittance, brightness and quantum degeneracy, which have direct ramifications to many setups and devices relying on pulsed coherent electrons.

Motivation & Objective

• To investigate the impact of Coulomb interactions on spatial coherence in ultrafast electron pulses from laser-triggered sources.
• To measure how electron bunch charge affects interference fringe visibility in few-electron regimes.
• To quantify the loss of spatial coherence and link it to effective source size via the van Cittert-Zernike theorem.
• To establish a general framework for coherence degradation in spatiotemporally confined electron beams.
• To enable improved design of ultrafast electron sources for applications in microscopy and quantum optics.

Proposed method

• Laser-triggered electron emission from a tungsten needle tip using 6 fs pulses at 80 MHz repetition rate.
• Use of a single-walled carbon nanotube (CNT) as an electrostatic biprism to split and interfere electron waves.
• Detection of interference fringes on a microchannel plate (MCP) screen to measure visibility.
• Systematic variation of laser power to control average electron charge per pulse while maintaining fixed geometry.
• Application of the van Cittert-Zernike theorem to relate fringe visibility to effective source size.
• Model simulations to quantitatively explain the observed coherence loss due to Coulomb repulsion.

Experimental results

Research questions

• RQ1 How does increasing electron bunch charge affect the spatial coherence of femtosecond electron pulses from a laser-triggered source?
• RQ2 To what extent do Coulomb interactions between electrons degrade interference visibility at sub-one-electron average charge?
• RQ3 Can the loss of coherence be quantitatively explained by an effective source size increase due to electron repulsion?
• RQ4 What is the role of stochastic emission (Poisson statistics) in inducing coherence loss even below one electron per pulse?
• RQ5 How do Coulomb interactions limit brightness and emittance in ultrafast electron sources?

Key findings

• Visibility of electron interference fringes decreases by 35% (to 65% of baseline) at an average of 1.4 electrons per pulse due to Coulomb repulsion.
• The loss of spatial coherence is quantitatively explained by an increase in the effective source size, as predicted by the van Cittert-Zernike theorem.
• Coulomb interactions cause a doubling of the effective source size at just 1.4 electrons per pulse, despite the low average charge.
• The coherence degradation is not due to quantum decoherence or classical dephasing, but due to stochastic, variable interaction phases from electron repulsion.
• The effect is observed even below one electron per pulse due to Poisson statistics, where two-electron events occur and induce visibility loss.
• The findings are general and independent of tip material or laser wavelength, applying broadly to ultrafast electron sources with strong spatiotemporal confinement.