An accessible tabletop source for the production of entangled x rays is crucial for the field of high-energy quantum optics. Here, we present a detailed analysis of the entanglement and polarization of the two photons emitted by an electron in an intense laser wave (nonlinear double-Compton scattering), by working within the framework of strong-field QED. By identifying contributions to the emission probability stemming from the electron being either on-shell or off-shell between the two-photon emissions, we show that the entangled photons are generated via the off-shell contribution for moderate beam energies, which are realizable on a tabletop setup. We propose an experiment to produce and isolate pairs of entangled x rays, through spectral filtering.
We study spin-spin entanglement in the final state photon-nucleon system in Compton scattering, both at low energy below the pion threshold and at high energy in perturbative QCD to next-to-leading order. We first establish a no-go theorem showing that, for any spin-
21 target, entanglement cannot be generated in unpolarized Compton scattering if the scattering amplitudes are real. We then consider polarized Compton scattering off the electron, the proton and the neutron. At low energy, we uncover a rich variety of maximally entangled Bell states and their unitary equivalents realized across different regions of the kinematic plane. Interestingly, the proton and neutron targets exhibit distinct patterns of entanglement. In the neutron case, the electric and magnetic polarizabilities dramatically influence the pattern and even the existence of entanglement. This suggests that entanglement can serve as a novel tool for investigating the detailed electromagnetic properties of the nucleons.