Multichannel Interference in Resonancelike Enhancement of High-Order Above-Threshold Ionization

The intensity-dependent resonancelike enhancement phenomenon in the high-order above-threshold ionization spectrum is a typical quantum effect for atoms or molecules in an intense laser field, which has not been well understood. The calculations of the time-dependent Schrödinger equation (TDSE) are in remarkable agreement with the experimental data, but they cannot clarify the contributions of the bound states. The semiclassical approach of strong field approximation, in which no excited states are involved, can obtain a similar phenomenon, but the laser intensities of enhanced regions predicted by the strong field approximation are inconsistent with the results of the TDSE. In this Letter, a new fully quantum model is established from the TDSE without any excited states. Two types of enhanced structures, unimodal and multimodal structures, are found in the results of the TDSE and model. In addition, the calculations of the model reproduce the key features of the results of the TDSE. It shows that the excited states are not the key factor in the resonancelike enhancements in our calculated system, since there are no excited states in our model. Based on the calculations of our model, we show that such resonancelike enhancements are caused by the constructive interference of different momentum transfer channels. Last, the Fano-like line shapes are also discussed for the features of multichannel interference.

Figure 1

Photoelectron energy spectra calculated by (a) TDSE, (b) SFA, and (c) model, as a function of the laser intensity or the parameter $(I_p+U_p)/\omega$. Three islands I, II, and ${\text{II}}^{\prime }$ are marked.

Figure 2

(Left) Normalized differential ionization rate calculated by (a) TDSE, (c) SFA, and (e) model as a function of $(I_p+U_p)/\omega$ for island I. (Right) Normalized differential ionization rate calculated by (b) TDSE, (d) SFA, and (f) model as a function of $(I_p+U_p)/\omega$ for island II. All the orders of ATI peaks, i.e., photon numbers absorbed by electrons, for different lines are labeled in (a).

Figure 3

Photoelectron energy spectra calculated by (a) Eq. (9), (b) Eq. (9) with the intensity of $W_{pg}$ kept as $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, and (c) Eq. (9) with the intensity of $V_{qp}^{*}$ kept as $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

(a) Differential ionization rate as a function of the laser intensity for the case of Fig. 1 (solid lines) and Fig. 3 (dotted lines) with photon numbers absorbed by electrons $n=80$, 85, and 90, where the results of different $n$ are multiplied by different multiples to facilitate separation. (b) The data and the fitting result as a function of the laser intensity for photon numbers $n=85$. The fitting parameters (c) $I_r$, (d) $\mathrm{\Gamma }$, (e) $R_b$, and (f) $q$ as a function of photon numbers.