Laser control of electron matter waves

In recent years laser light has been used to control the motion of electron waves. Electrons can now be diffracted by standing waves of light. Laser light in the vicinity of nanostructures is used to affect free electrons, for example, femto-second and atto-second laser-induced electrons are emitted from nanotips delivering coherent fast electron sources. Optical control of dispersion of the emitted electron waves, and optically controlled femto-second switches for ultrafast electron detection are proposed. The first steps towards electron accelerators and matter optics on-a-chip are now being taken. New research fields are driven by these new technologies. One example is the optical generation of electron pulses on-demand and quantum degenerate pulses. Another is the emerging development of interaction free electron microscopy. This review will focus on the field of free electron quantum optics with technologies at the interplay of lasers, electron matter waves, and nanostructures. Questions that motivate their development will also be addressed. This review will focus on the field of free electron quantum optics (FEQO) with technologies at the interplay of lasers, electron matter waves, and nanostructures. Recent developments that include laser generation, acceleration, coherent beam splitting, compression and detection of electron pulses with femto-second resolution are discussed. Some of the motivations for these developments concerning societal impact, finding solutions to long standing scientific problems, and speculative issues are indicated.