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Light-electron interaction in empty space is the seminal ingredient forfree-electron lasers and also for controlling electron beams to dynamicallyinvestigate materials and molecules. Pushing the coherent control of freeelectrons by light to unexplored timescales, below the attosecond, would enableunprecedented applications in light-assisted electron quantum circuits anddiagnostics at extremely small timescales, such as those governingintramolecular electronic motion and nuclear phenomena. We experimentallydemonstrate attosecond coherent manipulation of the electron wave function in atransmission electron microscope, and show that it can be pushed down to thezeptosecond regime with existing technology. We make a relativistic pulsedelectron beam interact in free space with an appropriately synthesizedsemi-infinite light field generated by two femtosecond laser pulses reflectedat the surface of a mirror and delayed by fractions of the optical cycle. Theamplitude and phase of the resulting coherent oscillations of the electronstates in energymomentum space are mapped via momentum-resolved ultrafastelectron energy-loss spectroscopy. The experimental results are in fullagreement with our theoretical framework for light-electron interaction, whichpredicts access to the zeptosecond timescale by combining semi-infinite X-rayfields with free electrons.

From attosecond to zeptosecond coherent control of free-electron wave functions using semi-infinite light fields