Coherence in multistate resonance-enhanced four-photon ionization of lithium atoms

A joint experimental and theoretical study of four-photon ionization of Li is performed using a pump-probe setup with the laser frequency tuned in between the excitation energies of the $2s$–$4p$ and $2s$–$4f$ three-photon transitions. The three-dimensional photoelectron momentum pattern is recorded as a function of the delay time between two otherwise identical laser pulses. The process is modeled by numerically solving the time-dependent Schrödinger equation. While complicated interference patterns arise in the electron spectrum when the two pulses partially overlap in time, the expected quantum-beat phenomenon between Li atoms in either the $4p$ or the $4f$ state are seen when the fast oscillations involving the $2s$ initial state are averaged over. The qualitative agreement between the predicted and observed beating patterns is very good.

Figure 1

Energy diagram of the Li atom with the relevant levels for the present study. The ionization is mediated by 3 + 1 REMPI through the virtual states (indicated by red bars) and the $4p$ and $4f$ levels reached by absorption of three photons.

Figure 2

Momentum distribution of the ejected electron for various delays between two linearly along the $z$ axis polarized 30-cycle laser pulses [see red arrow in (a)] with a peak intensity of ${10}^{11}$ W/cm${}^2$ and a sine-squared envelope of the electric field. The left and center columns exhibit the theoretical predictions at two time delays that differ by 0.46 fs (corresponding to the fast $2s$–$4p$ and $2s$–$4f$ period), while the right column shows the average of these two distributions. The time delays between the results displayed in the various rows and those from row 1 correspond to about 1/4 period (row 2), half a period (rows 3 and 4), and a full period (row 5) of the slow ($\approx 174$ fs in theory) $4p$–$4f$ beating period. Note that all color bars have the same scale.

Figure 3

Same as Fig. 2 for two partially overlapping laser pulses. Note the different scales on the color bars, which indicate the strong effect of the constructive or destructive interference due to the laser frequency. The panels shown cover about three laser periods.

Figure 4

Momentum distribution of the ejected electron after a single linearly polarized laser pulse of peak intensity $\approx 4\times {10}^{11}$ W/cm${}^2$ as observed in experiment (a) and theory (b). The respective peak normalized angular distributions (black: experiment; red: theory) are shown in (c).

Figure 5

Experimental (a) and theoretical (b) longitudinal momentum distributions of the ejected electron as function of the time delay between two linearly polarized 30-cycle laser pulses with a peak intensity of $\approx {10}^{11}$ W/cm${}^2$. Note that the original theoretical delays were rescaled (see text).

Figure 6

Momentum distribution of the ejected electron for a delay of 170 fs between two linearly polarized laser pulses of 30 fs (FWHM) duration, as observed in experiment (a) and theory (b). The experimental (black) and theoretical (red) peak normalized PADs are illustrated in (c).

Figure 7

Same as Fig. 6 for a delay of 270 fs.

Figure 8

Anisotropy parameters ${\beta }_2$ (a), ${\beta }_4$ (b), ${\beta }_6$ (c), and ${\beta }_8$ (d) as function of the pump-probe delay time. Experimental data (with error bars) are compared to the theoretical values (dashed lines) and the theoretical data convoluted with the experimental resolution (continuous lines). See text for details.