The Darkfield Approach to Measuring Vacuum Birefringence and Light-by-Light Couplings -- A Proof-of-Principle Experiment

TL;DR

This work validates a darkfield approach to measuring vacuum birefringence and light-by-light couplings by imprinting a central shadow in an XFEL beam and aligning a tightly focused pump to redistribute the quantum vacuum signal into a background-sparse region. The method relies on precise shadow quality, diffraction-aware imaging, and polarization-selective analysis to isolate the weak signal, enabling preliminary access to the low-energy constants $a$ and $b$ of the effective QED Lagrangian. The experimental implementation at the European XFEL/HEDEB demonstrates background suppression with shadow factors ${\cal S}$ in the $10^{-9}$ to $10^{-11}$ range (improved to $<3\times10^{-11}$ with small-pixel detectors) and good agreement with diffraction-based simulations, while polarization analysis confirms feasible separation of $\parallel$ and $\perp$ components. These results establish the practicality of dark-field measurements for quantum vacuum tests and outline a path toward polarization-resolved determinations of nonlinear QED effects with potential sensitivity improvements via higher pump energies and optimized beam parameters.

Abstract

Vacuum fluctuations give rise to effective nonlinear interactions between electromagnetic fields. These generically modify the characteristics of light traversing a strong-field region. X-ray free-electron lasers constitute a particularly promising probe, due to their brilliance, the possibility of precise control and favourable frequency scaling. However, the nonlinear vacuum response is very small even when probing a tightly focused high-intensity laser field with XFEL radiation and direct measurement of light-by-light scattering of real photons and the associated fundamental physics constants of the quantum vacuum has not been possible to date. Achieving a sufficiently good signal-to-background separation is key to a successful quantum vacuum experiment. To master this challenge, a darkfield detection concept has recently been proposed. Here we present the results of a proof-of-principle experiment validating this approach at the High Energy Density scientific instrument of the European X-Ray Free Electron Laser.

Figures (12)

• Figure 1: Idealized darkfield set-up with normalized intensity distributions at each critical plane indicated by a green arrow. The primary x-ray distributions (blue) are shown as for 4 planes with the dashed red line showing the laser focal intensity distribution. The central shadow is imprinted onto the x-ray probe beam by inserting an opaque beam stop ('obstacle'), transforming the initial distribution with a central maximum. In the focal plane a peaked distribution reappears with the shadow encoded in side-lobes appearing in the focus. At the interaction-point, IP, the central peak overlaps with the high intensity laser (ReLaX) focus. For matched x-ray and laser waists the resulting quantum vacuum signal (magenta line in the aperture plane) is peaked on axis, due to the suppression of the side-lobes in the interaction. An additional object O2 immediately after the first lens and matching aperture A2 in the image plane of O2 can also be introduced . In the experiment, the detectors are in the focus of lens 2.
• Figure 2: XFEL spectrum measured by the Hirex spectrometer. The SASE bandwidth is 25eV with seeded peak positioned at 8766eV with FWHM 0.7eV containing $86\%$ of the beam energy.
• Figure 3: Collimated XFEL beam profile on the detector plane.
• Figure 4: Focal intensity distribution of the full XFEL beam measured with ablation imprints (top panel). The bottom panels shows a lineout through the centre of the imprint (blue dots), and a theoretical fit (red line). The fit is an Airy focus with central peak diameter ($2w_0$) of 240 to which a small super Gaussian background representing the scattering background in the focusing lenses is added; see main text.
• Figure 5: Focal distribution of XFEL beam with 160µm electro-chemically polished tungsten wire as obstacle O1 and another as O2 after lens 1, simulation (top left panel), and reconstruction from the imprint measurement (top right). Both normalized. (lower panel) the central line out of the imprint measurements (blue dots), and the theoretical fit (red line) yielding an $1/e^2$ width ($2w_0$) of 180nm for the central peak.