Photon echo using imperfect x-ray pulse with phase fluctuation

Abstract

We study the impact of inter-pulse phase fluctuation in an x-ray free-electron laser on the signal in photon echo spectroscopy, which is one of the simplest nonlinear spectroscopic methods. A two-pulse echo model is considered with two-level atoms as the sample. The effect of both fluctuation amplitude and correlation strength of the random phase is studied both numerically and analytically. We find that the random phase leads to the changed amplitude and the unchanged rephasing time of the photon echo signal, and show that the relaxation time can be obtained with a previous photon echo setup by an additional average across the signals in different repeated measurements for the pulses with random phase.