Modal decomposition of a propagating matter wave via electron ptychography

TL;DR

This paper demonstrates experimentally that electron ptychography can decompose a partially coherent high-energy electron wave into independent modes, providing a full quantum mechanical description of its spatial coherence.

Contribution

It introduces a novel application of ptychography to decompose matter waves into modes and employs a density matrix framework for quantum mechanical analysis.

Findings

Successfully decomposed electron wave into independent modes

Measured the full spatial coherence of a propagating matter wave

Provided a quantum mechanical description of electron coherence

Abstract

We employ ptychography, a phase-retrieval imaging technique, to show experimentally for the first time that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wavefield. Here we use the density matrix to derive a formal quantum mechanical description of electron ptychography and use it to measure a full description of the spatial coherence of a propagating matter wavefield, at least to the within the fundamental uncertainties of the measurements we can obtain.