  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 Ramsey's 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.
