Tracing The Trajectory Of Photons Through Fourier Spectrum

How to record the trajectory of photons through a nondemolish measurement is a challenge in the modern wave-particle duality experiment.Many of the relevant attempts in history have been difficult to realize in experiment,and they have been in the imaginary stage.In 2013,the Israeli physicist Vaidman proposed a method to trace the trajectory of the photons through Fourier spectrum,and realized it in a nested interferometer.In this experiment,five mirrors,which vibrate at different frequencies and with small amplitude,are placed in the paths of the photons.The results of the study show that every vibrating mirror contributes a peak in the Fourier spectrum of the output beam,which is located at the vibrating frequency of the mirror,so long as this mirror ever interacts with the photons.Vaidman's analysis on the experimental data does not always provide us full or correct result on the photon's trajectory.Thesis,we develop this method by focusing on the centroid location of the output beam,real-time recording of its spatial position changes with CCD,and Fourier analysis of the real-time signal of this center position.Our results show that its Fourier spectrum could be used to reveal the trajectory of the photons.In the same nested interferometer,all five peaks appear in the spectrum,associated with the five vibrating mirrors,regardless of whether the output beam is constructive interference or destructive interference.During the simulation process,we also made different attempts for the vibration frequency of the mirror,which further determined the one-to-one correspondence between the peak and the vibration mirror.We believe that the modified method provides us more reliable information on the trajectory of the photons,and it is not limited by the vibration amplitude of the mirror,which is in favor of the potential applications.