Towards Entanglement of Free-Electron Pairs and Free-Electron–Bound-Electron Systems

Free-electron quantum optics [1] explores quantum-coherent interactions between free-electron wavepackets, light, and matter, enabling ultrafast and deep-subwavelength studies of quantum correlations. A central achievement of the field has been the realization of electron–photon entanglement [2–5]. Beyond this, theory has predicted entanglement between free electrons and bound electrons [6,7], as well as between pairs of free electrons through long-range Coulomb interactions [8]. While classical correlations between free-electron pairs were recently observed experimentally [9,10], direct evidence of residual entanglement remains elusive [8]. Likewise, free-electron–bound-electron entanglement has yet to be experimentally demonstrated [11,12].

In this talk, I will show that entangled free-electron pairs leave distinct signatures in the emitted light that directly depend on their quantum state [13], providing a route for optical detection of free-electron entanglement. I will then discuss recent experiments showing that Coulomb-entangled electron pairs driven by external laser fields exhibit characteristic two-dimensional quantum-walk–like energy-correlation patterns [8], clearly different from separable states. Next, I will present a new mechanism in which elastic interactions with electromagnetic fields generate entangled electron energy-comb states [14]. Finally, I will discuss how engineered electromagnetic environments can strongly enhance free-electron–bound-electron interactions [15,16], bringing experimental observation of this form of entanglement closer to reality.