# Photon-Photon Scattering at the High-Intensity Frontier: Paraxial Beams

## TL;DR

This paper investigates optical signatures of quantum vacuum nonlinearities using high-intensity laser beams, employing a numerical approach to predict signal photon characteristics for experimental verification.

## Contribution

It introduces a reliable numerical method to study photon emission signatures of QED vacuum nonlinearity in high-intensity laser collisions.

## Key findings

- Predicted total number of signal photons in laser collisions.
- Characterized spectrum, directions, and polarizations of emitted photons.
- Identified optimal setups with high background-to-noise ratios.

## Abstract

Our goal is to study optical signatures of quantum vacuum nonlinearities in strong macroscopic electromagnetic fields provided by high-intensity laser beams. The vacuum emission scheme is perfectly suited for this task as it naturally distinguishes between incident laser beams, described as classical electromagnetic fields driving the effect, and emitted signal photons encoding the signature of quantum vacuum nonlinearity. Using the Heisenberg-Euler effective action, our approach allows for a reliable study of photonic signatures of QED vacuum nonlinearity in the parameter regimes accessible by all-optical high-intensity laser experiments. To this end, we employ an efficient, flexible numerical algorithm, which allows for a detailed study of the signal photons emerging in the collision of focused paraxial high-intensity laser pulses. Due to the high accuracy of our numerical solutions we predict the total number of signal photons, but also have full access to the signal photons' characteristics, including their spectrum, propagation directions and polarizations. We discuss setups offering an excellent background-to-noise ratio, thus providing an important step towards the experimental verification of quantum vacuum nonlinearities.