We study the modulation enhancement of interaction and entanglement between distant atoms in the interaction between free electron and two-level atoms.
The modulation and engineering of the free-electron wave function bring new ingredients to the electron-matter interaction. We consider the dynamics of a free-electron passing by a two-level system fully quantum mechanically and study the enhancement of interaction from the modulation of the free-electron wave function. In the presence of resonant modulation of the free-electron wave function, we show that the electron energy loss and gain spectrum is greatly enhanced for a coherent initial state of the two-level system. Thus, a modulated electron can function as a probe of the atomic coherence. We further find that distantly separated two-level atoms can be entangled through interacting with the same free electron. Effects of modulation-induced enhancement can also be observed using a dilute beam of modulated electrons.
Free-Electron Bound-Electron Resonant Interaction (FEBERI) is the resonant inelastic interaction of periodically density-bunched free electrons with a quantum two level system. We present a comprehensive relativistic quantum mechanical theory for this interaction in a model in which the electrons are represented as quantum electron wavepackets (QEW). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wave-like interaction regimes, and manifesting the physical reality of the wavefunction dimensions and its density modulation characteristics in interaction with matter. The analysis comprehends the case of laser-beam-modulated multiple QEWs that are modulation-phase correlated. Based on the Born interpretation of the electron wavefunction we predict quantum transitions enhancement proportional to the number of electrons squared, analogous to superradiance.
We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron - bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is pre-shaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, crystal defect center, etc.) upon traversing in proximity to the target. Measurement of the post-interaction energy spectrum of the electrons, probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is the atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens new horizons for electron microscopy in material interrogation and quantum information technology.