Interference between multiple distinct paths is a defining property of quantum physics, where paths may involve actual physical trajectories, as in interferometry, or transitions between different internal (e.g. spin) states, or both. A hallmark of quantum coherent evolution is the possibility to interact with a system multiple times in a phase-preserving manner. This principle underpins powerful multi-dimensional optical and nuclear magnetic resonance spectroscopies and related techniques, including Ramseys method of separated oscillatory fields used in atomic clocks. Previously established for atomic, molecular and quantum dot systems, recent developments in the optical quantum state preparation of free electron beams suggest a transfer of such concepts to the realm of ultrafast electron imaging and spectroscopy. Here, we demonstrate the sequential coherent interaction of free electron states with two spatially separated, phase-controlled optical near-fields. Ultrashort electron pulses are acted upon in a tailored nanostructure featuring two near-field regions with anisotropic polarization response. The amplitude and relative phase of these two near-fields are independently controlled by the incident polarization state, allowing for constructive and destructive quantum interference of the subsequent interactions. Future implementations of such electron-light interferometers may yield unprecedented access to optically phase-resolved electronic dynamics and dephasing mechanisms with attosecond precision.
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