Electron dynamics from low-order harmonics generated by short laser pulses

Recently, low-order harmonics have gained much attention due to their applications as coherent light sources with a high repetition rate. In addition, the generation process is highly related to the bound electrons and can thus be applied to detect the dynamics of these electrons. In this work, we theoretically investigate the low-order harmonics below the first excited state, produced by a single-cycle optical pulse. We numerically solve the three-dimensional time-dependent Schrodinger equation (TDSE) to calculate the harmonic spectrum. With the help of a perturbation model, we can transparently understand the generation process of the spectrum. The results indicate that the harmonic spectrum can be sensitively influenced by the frequency component of the driving field. We find that the carrier envelope phase (CEP) dependence of low-order-harmonic generation originates from the interference of different harmonic orders. For these harmonics, the CEP effects can only be observed when the spectrum of the driving laser is extremely wide, which corresponds to the very short driving pulse. From the CEP-dependent interference structure, the phase relation of the third and the fifth harmonic can be extracted. The extracted information indicates that the atomic response induces a positive chirp for the emitted low-order harmonics. In addition, we investigated the harmonic phase calculated from the TDSE results. The harmonic phase is different from the phase predicted by the adiabatic model, and this phase difference can be related to the time delay of the electronic response. We extract the time delay from the harmonic phase and explore the CEP and intensity dependence of this time delay.