Phase Space Tomography of Matter-Wave Diffraction in the Talbot Regime

TL;DR

This paper presents a theoretical study on reconstructing the Wigner distribution function of large molecules in matter-wave interference, highlighting conditions for successful quantum state visualization despite experimental limitations.

Contribution

It introduces a numerical simulation method for WDF reconstruction in molecule Talbot-Lau interferometry, accounting for experimental imperfections and partial reconstructions.

Findings

Negativity observed in partially reconstructed WDFs.

Finite slit number and van der Waals interactions affect reconstruction quality.

Identifies experimental parameters for effective WDF reconstruction.

Abstract

We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already proves the wavelike behaviour of these heavy particles, while we aim to extract more quantitative information about the superposition quantum state in motion. We simulate the reconstruction of the WDF numerically based on an analytic probability distribution and investigate its properties by variation of parameters, which are relevant for the experiment. Even though the WDF described in the near-field experiment cannot be reconstructed completely, we observe negativity even in the partially reconstructed WDF. We further consider incoherent factors to simulate the experimental situation such as a finite number of slits, collimation, and particle-slit van der Waals interaction. From this we find experimental conditions to reconstruct the WDF from Talbot interference fringes in molecule Talbot-Lau interferometry.