Waveform control of relativistic electron dynamics in an underdense plasma

The interaction of ultra-intense laser pulses with an underdense plasma is used in laser-plasma acceleration to create compact sources of ultrashort pulses of relativistic electrons and X-rays. The accelerating structure is a plasma wave, or wakefield, that is excited by the laser ponderomotive force, a force that is usually assumed to depend solely on the laser envelope and not on its exact waveform. Here, we use near-single-cycle laser pulses with a controlled carrier-envelope-phase (CEP) to show that the actual waveform of the laser field has a clear impact on the plasma response. We measure relativistic electron beams that are found to be strongly CEP dependent, implying that we achieve waveform control of electron dynamics in underdense laser-plasma interaction. Our results pave the way to high precision, sub-cycle control of electron injection in plasma accelerators, enabling the production of attosecond relativistic electron bunches and X-rays.