# It is all about phases: ultrafast holographic photoelectron imaging

## TL;DR

This paper reviews ultrafast photoelectron holography, highlighting its advantages for high-resolution matter imaging, discussing its physical mechanisms, theoretical methods, and future challenges, with a focus on quantum interference and Coulomb effects.

## Contribution

It unifies the fragmented landscape of ultrafast photoelectron holography by providing a comprehensive review and connecting it with laser-induced electron diffraction.

## Key findings

- Holography enables subfemtosecond resolution imaging.
- Phase differences are used for reconstructing target information.
- The review emphasizes quantum interference and Coulomb effects.

## Abstract

Photoelectron holography constitutes a powerful tool for the ultrafast imaging of matter, as it combines high electron currents with subfemtosecond resolution, and gives information about transition amplitudes and phase shifts. Similarly to light holography, it uses the phase difference between the probe and the reference waves associated with qualitatively different ionization events for the reconstruction of the target and for ascertaining any changes that may occur. These are major advantages over other attosecond imaging techniques, which require elaborate interferometric schemes in order to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction (LIED) is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.