Observation of Feynman-path interference in high-order sideband generation

The quantum paths that satisfy the stationary phase condition of the Dirac–Feynmann path integral provide an intuitive picture in understanding extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG) and high-order terahertz sideband generation (HSG). Each order of high-order harmonics or sidebands can be essentially captured by a few quantum paths. In contrast to HHG, the process of HSG can be tailored delicately via controlling the excitation of the first step, which paves a way to regulate the recollisions of quantum paths. We report a scheme that invokes two beams of exciting fields, and their frequency difference is the even multiple of the driving-field frequency. We find that the number of spectroscopic dips is determined by the ratio of frequency difference to the driven-field frequency. And the positions of spectroscopic dips could be tuned elaborately by changing the initial phase difference between two exciting laser fields. This finding reveals a methodology to directly measure the amplitude of Feynman paths that contribute the high-order sidebands in the extreme nonlinear optics regime.