Simulations of Photon Echoes in support of Atomic Lifetime Measurements

We have recently reported measurements of the Rb 5P_3/2 excited state lifetime with a statistical uncertainty of 0.11% based on the technique of photon echoes (Beica et al., Phys Rev A 101, 033408, (2020)). The experiment relies on measuring the exponential decay of the photon echo intensity as a function of the time separation T between two, 12 ns excitation pulses. To understand systematic uncertainties, we have simulated this experiment using optical Bloch equations that include damping and effects of pulse propagation. These simulations successfully model pulse compression, the breakup of pulses due to the McCall-Hahn area theorem, and the change in pulse areas as a function of optical depth. We use the results of these simulations to study the dependence of the echo intensity on experimental parameters such as pulse areas, density, laser linewidth, and transit time. We also investigate the effects of the first excitation pulse on the propagation of the second excitation pulse to improve background subtraction in the experiment.