Simulating vacuum birefringence with a diffractive beam propagation code

TL;DR

The paper addresses the challenge of directly observing quantum vacuum nonlinearities in macroscopic electromagnetic fields by integrating a vacuum emission module (VIBE) into the diffractive beam propagation framework LightPipes. Building on the Heisenberg–Euler Lagrangian in the weak-field regime, it derives a compact, Fresnel-Kirchhoff–type signal expression for the dominant vacuum signal in pump–probe collisions and demonstrates how to propagate both signal and probe through realistic optical elements. The authors validate their approach against analytic benchmarks and showcase a realistic, experimentally relevant scenario involving an XFEL probe and an IR pump, including optical components and a dark-field arrangement. The work provides a practical and efficient tool for planning and interpreting vacuum birefringence experiments, enabling large-scale parameter studies and robust treatment of experimental imperfections.

Abstract

Ninety years after their prediction, quantum vacuum nonlinearities in macroscopic electromagnetic fields still await a direct experimental verification in the laboratory. A particularly promising route towards their first measurement is the collision of counter-propagating laser beams in a pump-probe type experiment. Here, the key challenge is to separate the small quantum vacuum signal at the oscillation frequency of the probe that is mainly emitted in the vicinity of its forward cone from the large probe background. While quantitatively accurate predictions of the associated quantum vacuum signals are available, to date there is no framework that combines these predictions with a diffractive beam propagation code. Such codes are designed to holistically model optical experiments and can reliably account for diffraction and absorption losses of optical devices, like lenses and apertures. The latter inevitably influence and modify both the induced signal and background components prior to their detection in experiment. The present work addresses this topical issue and reports on the first implementation of a quantum vacuum signals emission module in an established diffractive beam propagation toolkit designed for the realistic modelling of optical experiments.

Figures (3)

• Figure 1: Schematic illustration of the vacuum emission module VIBE implemented in the diffractive beam propagation toolbox LightPipes.
• Figure 2: Idealized example scenario of a pump-probe interaction generating a quantum vacuum signal. (a) Side view of the probe (blue) and quantum-vacuum signal (multicolour) intensity maps. The signal is generated in the interaction region at ${\rm z}=0$ and co-propagates with the probe towards ${\rm z}>0$. Transverse profiles of the (b) probe and (c) signal photon distributions in the detection plane at ${\rm z}=4\,{\rm m}$. (d) Lineout through the peak value of the signal photon distribution. The black solid line is extracted from the simulation outcome (c), and the red-dotted line is the result of an analytical benchmark calculation.
• Figure 3: Data-driven simulation of an experimental setup devised to measure the quantum vacuum signal generated in a pump-probe interaction. (a) Side view of the probe (blue) and quantum-vacuum signal (multicolour) intensity maps. Transmission of the (b) probe and (c) signal through the setup. These panels also provide the transmissions of the individual objects inserted in the beam path. Transverse profiles of the (d) initial and (e) focussed probe. (f) Focus profile of the pump. Distribution of the ($\perp$-polarized) quantum vacuum signal (g) right before the slit and (h) in the detector plane.