Control of nonlinear Compton scattering in a squeezed vacuum

Electromagnetic radiation by accelerated charges is a fundamental process in physics. Here, we introduce a quantum-optical framework for controlling the emission of radiation of an electron in an intense laser field via squeezed vacuum states. By engineering the quantum fluctuations of the emission modes, we demonstrate that the probability of nonlinear Compton scattering can be significantly enhanced or suppressed through tunable squeezing amplitude and angle. Our predictions are experimentally accessible with current squeezing technologies, establishing a new paradigm for quantum control in high-intensity light-matter interactions.