Probing vacuum birefringence in an Ultrastrong Laser Field via High-energy Gamma-ray Polarimetry

Abstract

Vacuum birefringence (VB), a fundamental prediction of nonlinear quantum electrodynamics (QED), has eluded direct laboratory detection due to its extreme weakness. We propose a compact, "self-probing" scheme where a GeV electron beam collides head-on with a petawatt laser pulse. Circularly polarized gamma-ray photons, generated via nonlinear Compton scattering in the same pulse, then probe the birefringent vacuum it induces. This integrated design bypasses the stringent synchronization and beam transport requirements of traditional pump-probe setups. Our nonperturbative strong-field QED simulations reveal a clear VB signature: conversion of circular to linear polarization, with the induced Stokes parameter $S_1$ reaching ~0.019 within the selected angular range. This corresponds to a refractive index difference $Δn = 1.829 \times 10^{-4}$ over micron-scale paths, directly measurable as a high-contrast "X-shape" asymmetry in $e^+e^-$ pair distributions. The scheme provides a feasible path to first laboratory VB detection with current laser and accelerator technologies.

Figures (6)

• Figure 1: Schematic of the simulation setup. A longitudinally polarized electron beam collides head-on with a high-intensity, linearly polarized laser pulse. The interaction generates high-energy $\gamma$-photons that are initially predominantly circularly polarized (large Stokes parameter $S_2$). As these photons propagate through the remaining laser field, vacuum birefringence (VB) induces a phase difference between polarization components parallel and perpendicular to the laser's electric field. This causes the photons' polarization state to evolve from circular toward elliptical, manifesting as a decrease in $S_2$ and the appearance of a measurable linear polarization component ($S_1$). The evolution of the Stokes parameters $(S_1, S_2, S_3)$ fully captures this polarization transformation.
• Figure 2: Angular distributions of (a) photon energy, (b) photon number, (c) Stokes parameter $S_1$, and (d) $S_2$ from the full simulation including VP. Panels (e) and (f) show the corresponding $S_1$ and $S_2$ distributions when VP effects are artificially disabled. The dashed rectangle in all panels indicates the selection region applied to isolate high-energy photons for analysis, spanning $\pm10$ mrad in both horizontal and vertical divergence angles ($\theta_x, \theta_y \in [-10,10]$ mrad).
• Figure 3: Signature of VB. Stokes parameters (a) $S_1$, (b) $S_2$, (c) $S_3$, and (d) $S_1/S_2$ as functions of photon energy for photons within the angular selection region of Figure. \ref{['fig:angular_distribution']}. Red curves: results including VP (both VB and VD). Blue curves: results with VP artificially disabled.
• Figure 4: (a) Evolution of the Stokes parameter $S_1$ as a function of the laser phase $\eta = \omega_0 t - k_0 z$ for a 1 GeV photon. Red solid line: full Monte Carlo simulation including both VB and VD. Blue dashed line: deterministic integration of the VP-induced phase shift based on the nonperturbative polarization operator (Eqs. \ref{['eq:VB_rotation']} and Eqs. \ref{['eq:VD']}). Blue solid line: contribution from VD alone, obtained by Eqs. \ref{['eq:VD']}. (b) Comparison of the instantaneous polarization rotation rates $dS_1/dt$ arising from VB and VD as a function of the quantum parameter $\chi_\gamma$ for the same 1.341 GeV photon. The dots represent simulation data. The color gradient of the points reflects the evolution of the laser phase (interaction time).
• Figure 5: Required initial electron number $N_e$ for a $5\sigma$ VB signal, plotted against (a) spot size $w_0$, (b) pulse duration $\tau_p$, (c) initial electron polarization, and (d) electron beam energy $E_e$.