Manipulation of Superposed Vortex States of $\gamma$ Photon via Nonlinear Compton Scattering

Vortex $\gamma$ photons in superposition states have important applications in photonuclear, high-energy, and strong-field physics. However, their controlled generation in the $\gamma$-ray regime remains a great challenge. Here, we put forward a novel method for the generation of vortex $\gamma$ photon in superposition states, with controllable orbital angular momentum (OAM) separation $\Delta\ell^\prime$ and modal weights, via nonlinear Compton scattering driven by multifrequency circularly polarized laser fields. We develop a strong-field quantum electrodynamics (QED) framework to reveal the underlying mechanism and calculate the radiation probabilities. In our method, the superposition arises from interference between energy-degenerate multiphoton pathways carrying distinct OAM. For two-frequency fields, the OAM separation follows $\Delta\ell'=\nu\mp1$ (upper/lower sign for equal/opposite helicities), and modal weights are tunable by laser intensities, with $\nu$ the frequency ratio. Vortex $\gamma$ photons in controllable superposition states from our method have significant applications in strong-field QED and nuclear photonics.