Photoelectron spectra and high Rydberg states of lithium generated by intense lasers in the over-the-barrier ionization regime

We calculated photoelectron energy and momentum spectra and the population of high Rydberg states of lithium atoms by intense 785 nm laser pulses at intensities in the over-the-barrier ionization (OBI) regime. The calculated spectra are compared to experiments reported in Schuricke et al. [Phys. Rev. A 83, 023413 (2011)]. It is shown that in the OBI regime, due to strong depletion of the ground state, the photoelectron spectra are generated from the leading edge of the laser pulse only, resulting in spectra that are nearly independent of laser intensities. Analysis of the calculated spectra reveals that total ionization probability is suppressed as the intensity is increased in the OBI regime. The suppression is due to the increase of excitation probability of high Rydberg states in the OBI regime, demonstrating that atoms and molecules are never fully ionized at high intensities. We also conclude that the interference stabilization model is not needed to explain the formation of high Rydberg states, and that there is no evidence that laser-dressed Kramers-Henneberger states play a role in the strong-field ionization of atoms and molecules by infrared lasers in the OBI regime.

Figure 1

Single intensity excitation and ionization probabilities obtained by solving the TDSE for a Li atom exposed to a 785 nm/30 fs laser pulse. Notable features are (1) three-photon Rabi oscillations between 2$s$ and 4$f$, (2) full depletion of the 2$s$ ground state beyond 6 TW/cm${}^2$, and of the 4$f$ state beyond 8 TW/cm${}^2$, and (3) ionization suppression accompanied by growth of Rydberg states at intensities beyond 8 TW/cm${}^2$. Note that atoms are not fully ionized in intense laser fields and survive by staying in Rydberg states.

Figure 2

Time dependence of the probability of the field-free 2$s$ state during the laser pulse: (a) Input laser's electric field; (b), (c) 2$s$ survival probability as a function of time for different input intensity.

Figure 3

Illustration of the differential intensity contributions to the ionization yield, weighted by the volume element, for a focused laser beam with various peak intensities at the focus. Due to strong depletion, at high peak intensities at the focus, the distributions are very similar.

Figure 4

Comparison of theoretical and experimental photoelectron energy spectra at different peak intensities at the laser focus. The experiment is from Schuricke et al.[4]. Note that the photoelectron spectrum is dominated by the four-photon absorption peak, with a minor contribution from the five-photon absorption peak, for intensities from 4–70 TW/cm${}^2$. The theory results are from solving the TDSE and include contributions from the whole laser focus volume. The remaining discrepancy is likely due to the fact that parameters for spatial and temporal distributions of the input laser between theory and experiments are not exactly identical.

Figure 5

Comparison of experimental (top row) and theoretical (bottom row) 2D momentum spectra for different peak intensities. Note that main features of the angular distributions have not changed over the intensities shown. The theoretical spectra are broader than the experimental data. We found (not shown) that better agreement with experimental data can be seen if the simulation is carried out with half of the indicated experimental peak intensity. Volume effect has been considered in the theoretical calculation.

Figure 6

Expanded photoelectron energy spectra at selected intensities. The nonresonant four-photon absorption peak is shown to display the shift to lower energy with increasing intensity, while the main 4$f$ and 5$f$ Freeman resonances are clearly seen in the calculation. Fainter features at higher energies are more difficult to identify. Above 8 TW/cm${}^2$, i.e., above the $\eta$-OBI threshold, the four-photon absorption peak position does not change with input peak intensity because of ionization depletion before the pulse is over. In fact, its peak position shifts slightly to higher energy.

Figure 7

Theoretical 2D momentum spectra at selected intensities shown. Note the presence of split fine structures within the ATI peak.

Figure 8

(a) Distributions of high Rydberg states for Li exposed to 30 fs/785 nm laser at intensity of 10 TW/cm${}^2$. (b) The same, but at 7 TW/cm${}^2$. The arrows and integers indicate the positions of the Rydberg states. (c) Display of excitation probability distributions for Rydberg states and low-energy electrons at several peak intensities. The distributions below the ionization threshold decide the populations of Rydberg states generated by the laser. (d) Population density across the ionization threshold at 10 TW/cm${}^2$. A smooth curve is drawn across the threshold for each orbital angular momentum of the electron.