Frontier Science Working Groups

# High-Field Physics and Quantum Electrodynamics (HFP/QED)

The HFP/QED working group investigates fascinating phenomena predicted by quantum electrodynamics (QED) in intense electromagnetic fields and how to put them under experimental scrutiny at NSF OPAL, including the nonlinear properties of the quantum vacuum, the influence of the radiation emitted by a charge on the dynamic of the charge itself, and the possibility of materialization of laser energy into electron-positron pairs.

FLAGSHIP EXPERIMENT

## Stimulated Photon-Photon Scattering

Quantum electrodynamics (QED) predicts that electromagnetic (EM) fields may interact in vacuum, with the interaction mediated by virtual pairs of charged particles and antiparticles. This so-called ‘vacuum nonlinearity’ is a purely quantum effect: the classical Maxwell’s equations in vacuum are strictly linear. The idea that the existence of particle/antiparticle fields gives rise to nonlinear effects in the propagation of EM fields in vacuum was formulated in Refs. [1,2], where the quantum Lagrangian density of a slowly-varying EM field was determined including the electron-positron “vacuum fluctuations.” This is the renowned Euler-Heisenberg Lagrangian density.[3]

The importance of the nonlinear terms in the Euler-Heisenberg Lagrangian density is determined by the strength of the EM field relative to the so-called “critical” electric and magnetic fields of QED: E_{cr} = m^{2}c^{3}/ℏ|e| ≈ 1.3×10^{16} V/cm, and B_{cr} = m^{2}c^{3}/ℏ|e| ≈ 4.4×10^{13} G. The critical fields exceed by orders of magnitude the most intense EM fields ever produced in the laboratory by high-power lasers: the world-record for laser intensity is presently about 1×10^{23} W/cm^{2}, which corresponds to an electric field amplitude of approximately 6×10^{12} V/cm. This explains why vacuum-nonlinearity effects are typically very small and challenging to measure. In particular, the lowest-order nonlinear vacuum interaction between two photons requires a closed fermion loop with four vertices. This makes photon-photon scattering highly suppressed with respect to, e.g., electron-photon scattering. For optical photons (ℏω ≈ 1 eV), the scattering cross-section is calculated to be σ_{γγ} = [7.3×10^{-66} cm^{2}] (ℏω/eV)^{6}.[4] While upper-bound results exist in the literature, no realistic attempt to measure direct photon-photon scattering has been made to date.

We propose to use the unprecedented 2×25 PW laser power of the NSF OPAL facility to directly measure photon-photon scattering for the first time, using the stimulated photon-photon scattering (SPPS) concept. In this design, three laser beams collide, one of which acts as a “stimulating” beam along which one of the two scattered photons is emitted. The SPPS process is analogous to non-linear 4-wave mixing in the quantum vacuum, and has the advantage that the scattered photon signal propagates in a known direction that is distinct from the incident lasers. We predict NSF OPAL to produce a signal exceeding 1000 scattered photons per shot: this is high enough to avoid reliance on statistical methods to interpret the result, and to permit a detailed study of the SPPS interaction over a range of parameters. If successful, this Flagship experiment will provide a direct measurement of nonlinear effects in the quantum vacuum. These results will confirm a century-old prediction of quantum field theory.

- W. Heisenberg and H. Euler, Z. Physik 98, 714 (1936). doi: 10.1007/BF01343663.
- V. Weisskopf, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 14, 1 (1936).
- J. Schwinger, Phys. Rev. 82, 664 (1951). doi: 10.1103/PhysRev.82.664.
- V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics. Elsevier Butterworth-Heinemann, Oxford, 1982.

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