Real-time lattice scalar QED simulations of recoil effects in laser-plasma scatterings

When free-electron lasers interact with solid-density plasmas, or when optical lasers collide with charged bunches, relativistic quantum effects are important. Existing numerical methods, such as quantum electrodynamics (QED) particle-in-cell (PIC), treat charges and fields self-consistently only when they interact via Lorentz force law and Maxwell’s equations. Additional processes, such as radiation reactions, are added separately but not treated self-consistently. In this work, we develop real-time lattice QED simulations that treat all processes self consistently. We focus on scalar QED, which adequately describes plasmas above Fermi degeneracy. We solve the coupled Klein-Gordon-Maxwell equations as initial-boundary value problems. A many-body wave function is constructed from single-particle orbitals to model collective plasma effects. Each orbital represents a collection of physical particles, much like macroparticles in PIC. However, unlike PIC, the orbitals resolve particles’ quantum wave packets, capturing QED processes from first principle. We apply lattice QED to simulate laser-plasma scatterings and demonstrate recoil effects on electron spectrum during nonlinear Compton scattering, and on laser spectrum during x-ray Raman scattering.