Fig. 4: Experimental demonstrations of free-electron–photon measurements in the quantum (PINEM) and the classical (DLA) cases.
From: Weak measurements and quantum-to-classical transitions in free electron–photon interactions
a The schematic setup of UTEM with a prism-mediated laser-near-field electron interaction used to obtain the PINEM spectrum. b The schematic setup of the DLA-based experiment with two gratings (modulator and analyzer) was used to obtain net electron acceleration. c The symmetric energy spectrum with sideband spacing of \({\hslash }\omega\)(1.7eV) indicates the quantum regime of the electron–photon interaction. The data (bottom panel) matches well with the PINEM theory of wide electrons in the plane-wave limit, the simulation results of which are shown in the top panel. d The left panel shows the net energy transfer as a function of the modulator peak field and for a constant analyzer peak field of 207 MV/m. Figure S2 of the Supplementary Information shows simulation data with a similar behavior, hence this behavior shows the transition from unbunched to bunched electron beams. With a maximum modulator field strength of 224 MV/m here, the bunched pulse duration is around 1.1 fs, considerably smaller than the optical cycle (6.45 fs), thus showing the point-particle classicality of the bunched electrons. The right panel shows the energy gain for both the acceleration peak and the maximum 5% (see Fig. S4 in the SI file) for a modulator peak field of 224 MV/m. Both depend linearly on the analyzer’s field strength, demonstrating the weak value measurement of the photon system. The “5% maximum” is the maximum peak acceleration at 5% of the count rate
