Framework of the interaction between free electrons and confined electrons in cavity quantum materials

The interaction between free electrons and photons continues to attract significant research interest due to its potential applications in ultrafast dynamics probing, the generation of exotic quantum optical states, and quantum computing. In addition, it is demonstrated that cavity vacuum photons can significantly modify material properties through the formation of quantum-vacuum-dressed states in the ultrastrong coupling regime; however, coupling free electrons to cavity-dressed vacuum states remains elusive due to the three-body complexities, which currently hampers efforts to probe confined photon-electrons in cavity quantum materials. This work establishes a general framework for investigating interactions between free electrons and confined electrons in cavity quantum materials. We examine the dynamics of free electron scattering with a hybrid light—matter system, demonstrating that the strong coupling hybridized states significantly modify the free electron energy loss spectrum and generating free-electron—photon—matter entanglement. This modification offers a pathway to probe the altered properties of hybridized states, revealing a promising method for probing and manipulating cavity—matter systems.