High-Energy Vacuum Birefringence and Dichroism in an Ultrastrong Laser Field

A long-standing prediction of quantum electrodynamics, yet to be experimentally observed, is the interaction between real photons in vacuum. As a consequence of this interaction, the vacuum is expected to become birefringent and dichroic if a strong laser field polarizes its virtual particle–antiparticle dipoles. Here, we derive how a generally polarized probe photon beam is influenced by both vacuum birefringence and dichroism in a strong linearly polarized plane-wave laser field. Furthermore, we consider an experimental scheme to measure these effects in the nonperturbative high-energy regime, where the Euler-Heisenberg approximation breaks down. By employing circularly polarized high-energy probe photons, as opposed to the conventionally considered linearly polarized ones, the feasibility of quantitatively confirming the prediction of nonlinear QED for vacuum birefringence at the $5\sigma$ confidence level on the time scale of a few days is demonstrated for upcoming 10 PW laser systems. Finally, dichroism and anomalous dispersion in vacuum are shown to be accessible at these facilities.

Figure 1

The Euler-Heisenberg effective action is only valid for approximately constant fields (denoted by a wiggly line with a cross). The polarization operator must be considered if the momentum of the probe photon (wiggly line) becomes influential ($\chi \gtrsim 1$). Here, a solid double line denotes the exact electron propagator inside a classical background field.

Figure 2

A background field changes the photon dispersion relation via radiative corrections induced by virtual particles [2]. Here, we neglect higher-order radiative corrections to the electron-positron loop as $\alpha {\chi }^{2/3}\ll 1$ [11].

Figure 3

(a) Experimental setup. Polarized highly energetic gamma photons (produced via Compton backscattering) propagate through a strong laser field, which induces vacuum birefringence and dichroism. Afterward, the gamma photons are converted into electron-positron pairs. From their azimuthal distribution, the polarization state is deduced. (b) Regions of the transverse plane (gray), which are used to define the observables $R_B$ (left) and $R_D$ (right) [see Eq. (13)].

Figure 4

Plot of $\delta \varphi$ as a function of $\chi$ and $\xi N$ for a rectangular pulse profile. For each of the three laser facilities, gamma photons with energy $\omega =0.1\mathrm{GeV}$ (left point), $\omega =0.5\mathrm{GeV}$ (central point), and $\omega =1\mathrm{GeV}$ (right point) are indicated. Note that $|\delta \varphi |\gtrsim 0.1$ is also achievable by employing a longer PW laser pulse (e.g., National Ignition Facility with $\mathrm{\Delta }t=3\mathrm{ns}$ [32]) and probe photons with $\omega \gtrsim 0.1\mathrm{GeV}$.

Figure 5

Final Stokes parameters [see Eq. (11)] for gamma photons propagating through an ELI-NP 10 PW laser pulse ($S^{(0)}=\{1,0,-1,0\}$). The strongest effect is obtained around $\chi =1$ (note that pair production becomes sizable for $\chi \gtrsim 1$). As we consider the tunneling regime $1/\xi \ll 1$, cusplike structures—characteristic for multiphoton pair production [18, 65]—are absent.