Quantum Optical Electron Pulse Shaper

TL;DR

This work proposes a quantum-optical approach to freely propagating electron pulse shaping by letting a partially coherent electron interact with a light field whose frequency is time-dependent, inducing a phase modulation that creates energy sidebands spaced by $\hbar\omega(\tau)$. By controlling the light pulse envelope $I(\tau)$ and its instantaneous frequency $\omega(\tau)$, the method enables arbitrary time–energy shaping of the electron wave packet, including compression to a few femtoseconds without broadening the electron energy bandwidth. The authors develop a formal framework using energy-time representations and Wigner functions, demonstrate chirp-inversion-based compression for 5 keV electrons, and show how short-pulse gating and periodic gating can produce trains of attosecond- to femtosecond-scale electron sub-pulses. The approach promises ultrafast imaging and diffraction with high time, spatial, and spectral resolution, bridging optical pulse-shaping techniques to pulsed-electron applications.

Abstract

Coherent control of ultrafast quantum phenomena benefits from pulse-shaping capabilities allowing to modulate the envelope and instantaneous phase of optical fields on femtosecond time scales. While such control is available for optical fields, an analogy of a pulse shaper for freely propagating electrons is lacking. In this study, we theoretically demonstrate a method that enables near arbitrary light-based shaping of electron wave packets in the time domain. The method is based on the quantum phase modulation of electron waves by coherent light with time-dependent frequency leading to generation of spectrally separated electron energy side bands with shaped time-energy profiles and envelopes. Our results show that few femtosecond time durations can be achieved without additional spectral broadening of the electron wave packet, allowing one to reach the combination of high time, spatial, and spectral resolutions in ultrafast imaging and diffraction experiments with pulsed electron beams.

Figures (8)

• Figure 1: (a) An electron pulse with finite spectral width is generated via short pulse emission from the tip. (b) The electron pulse acquires a positive chirp through dispersive propagation. At the interaction site the electron pulse traverses a dielectric membrane e.g., illuminated by an optical pulse with modulated instantaneous photon energy $\hbar \omega(\tau)$ and intensity envelope $I(\tau)$. (c) The absorptions (emission) of photon quanta result in the generation of tailored energy sidebands. (d) After propagating for a certain distance, the quesi-probability side bands are reshaped.
• Figure 2: Spectrogram representation of the electron pulse (a) dispersion-free, with total pulse duration of 9.9 FWHM, (b) with group delay dispersion $\alpha$ and total duration of 250 fs FWHM, (c) the electron side-bands after interaction with the optical field, (d) after propagation, (e) close-up of the compressed sideband spectrogram. We note that in the spectrogram representation the sidebands are elongated in the $\tau$-direction due to the convolution with Gaussian kernel.
• Figure 3: Spectrogram of the electron pulse with 242 fs FWHM with linear and nonlinear chirp (a) after interaction with linearly chirped light (GDD only) (b) after interaction with light with GDD and TGD (c) GDD compensated after propagation for 21 cm, compression to 13 fs FWHM (d) after propagation for 21, GDD and TGD compensated, compressed down to 11 fs.
• Figure 4: (a) Spectrogram of the long initial pulse with FWHM duration 50 fs, (b) of the chirped electron pulse after interaction with a short optical pulse, (c) of the electron pulse state after propagation in free space for $\approx$ 32 cm, (d) close up of the compressed sideband with FWHM temporal duration of $\approx$ 10 fs. Spectrograms (e) of the electron pulse state after interaction with phase- and amplitude-modulated optical field, (f) after propagation for 21 cm, (g) close up of the compressed pulse train.
• Figure 5: Comparison of the ideal and the down-sampled and frequency-restricted spectrum of light pulse with GDD and TOD.