Nonlinear Compton Scattering in a Quantized Pump Field

Traditional strong-field quantum electrodynamics (QED) treats the driving laser as a classical, prescribed background field. This paper addresses the fundamental question of how nonlinear Compton scattering (NLC) changes when the driving laser is instead treated as a quantized degree of freedom. By incorporating the pump into the Hilbert space, the study aims to account for effects like pump depletion, back-action, and entanglement between the electron, the pump, and the emitted radiation.

To solve this, the author develops a fully quantized Furry-picture formulation. The electron is described by quantum-Volkov states—dressed states that include the pump's photon-number structure. The interaction is modeled as a transition between these dressed states, where the pump is retained as a dynamical subsystem. The author derives exact solutions for both circularly and linearly polarized pumps and, for bright pumps where direct summation is computationally expensive, derives a Wigner-Weyl reduction that expresses the scattering probability as a weighted average of coherent-state results.

• Quantized Dynamics: Unlike classical theory, the quantized pump formulation explicitly tracks photon-number transitions, allowing for the calculation of pump depletion and correlations between emitted particles and the residual pump.
• Spectral Features: A finite Fock-state pump imposes discrete photon-transfer edges and a terminal spectral cutoff, features absent in classical models.
• Wigner-Weyl Reduction: In the bright, weakly depleted regime, the complex quantum dynamics simplify to a Wigner-function weighted average of classical scattering probabilities. This allows for the inclusion of initial amplitude and phase fluctuations of the pump.
• Squeezing Effects: For squeezed coherent light, the squeezing angle and magnitude directly reshape the photon-number fluctuations, which in turn modifies the harmonic spectrum and high-energy emission yield.