Vacuum birefringence in high-energy laser-electron collisions

Real photon-photon scattering is a long-predicted phenomenon that is being searched for in experiment in the form of a birefringent vacuum at optical and x-ray frequencies. We present results of calculations and numerical simulations for a scenario to measure this effect using multi-MeV photons generated in the collision of electrons with a laser pulse. We find that the birefringence of the vacuum should be measurable using experimental parameters attainable in the near future.

Figure 1

Schematic of the envisaged two-stage setup to measure vacuum birefringence in high-energy photons. $a_1=(0,\varepsilon )$ and $a_2=(0,\beta )$ are the polarization directions of the external field in each stage.

Figure 2

Left: electrons (black thin trails) and photons (blue thick straight lines) produced in stage I of the simulation. Right: color $x-y$ plot of the photon angular distribution and energy spectrum of photons with a line plot of how the frequency distribution $\omega \partial N_{\gamma }/\partial \omega$ compares with theory for polarizations $e_1$ (upper two curves) and $e_2$ (lower two curves). The probability for photon emission by each electron is assumed to be incoherent, i.e., $N_{\gamma }=N_e{P}_{\gamma }$. This and later plots were generated with matplotlib [43].

Figure 3

The normalized cumulative distribution of photons at the end of stage I (solid lines) and the corresponding distribution in a CCF (dashed line). Lower values of ${\chi }_p$ have a larger proportion of softer photons.

Figure 4

Spectra obtained with the new event generator compared with stage I run for 100 initial electrons of energy 500 MeV, with ${\xi }_1=100,{\sigma }_1=8\pi$, and an initial electron offset of $z_0={\sigma }_1$. $N_{\gamma ,1}$ $\left(N_{\gamma ,2}\right)$ refers to photons created in the $e_1$ $\left(e_2\right)$ eigenstate. Bars (lines) plot values using the new (old) event generator. $N_{\gamma ,1}=2510$ (2020) and $N_{\gamma ,2}=687$ (513) for the new (old) event generator.

Figure 5

Simulation and theory results for stage II of Fig. 1. At the end of stage II, simulation predicts $\langle U\rangle =0.125$, and theory predicts $\langle U\rangle =0.128$. The background color signifies $U$ for photon frequency given by the lower horizontal axis in units of the electron mass. The line along the left vertical axis is the shape of the laser background envelope. Dashed lines represent the calculations from theory, which assume photons counterpropagate with the background; solid lines are results from simulation.

Figure 6

Average Stokes parameter after stage II. Theory predicts saturation of the effect to begin in the shaded region.

Figure 7

Average Stokes parameter after stage II for the accelerator setup with ${\xi }_1=0.36$ and ${\sigma }_1=17\pi$ $\left(15\mathrm{fs}\right)$. The shaded region corresponds to where theory predicts the onset of saturation.