Spatial-temporal control of interferences of multiple tunneling photoelectron wave packets

We theoretically study the control of the interferences of multiple tunneling photoelectron wave packets in both temporal and spatial domains by an orthogonally polarized two-color laser pulse. Profound carpetlike and stripelike interference patterns can be turned on or off in the momentum spectra using a weak streaking field at half the frequency of a strong fundamental field. The modulations of the interference patterns with respect to the relative phase between the two frequency components are well recaptured by both a semiclassical interference model and an ab initio simulation with numerically solving the time-dependent Schrödinger equation. We highlight the importance of the ionic Coulomb potential on the photoelectron angular distributions of atoms in the orthogonally polarized two-color pulses. It is shown that the interference induced by the forward rescattering trajectories is enhanced while the contribution of the direct trajectories is suppressed. This study offers alternative routes toward probing and controlling the ultrafast ionization dynamics of atoms and molecules.

Figure 1

(a) Separating multiple tunneling wave packets that are produced by a strong 800-nm field using a weak streaking field at 1600 nm. Each cycle of the OTC pulse (blue area) launches four electron wave packets (black for w1, red for w2, gray for w3, and green for w4) through the tunneling near the field maximum. The weak 1600-nm streaking field steers the electron motion in the lateral direction (indicated by the blue arrow), as shown by the trajectories of the four wave packets. Also shown are the simulated photoelectron angular distributions by the semiclassical model (b) without and (c) with the Coulomb potential. Here the interference effect is ignored. The field-driven photoelectron momenta $\mathbf{p}=-\mathbf{A}\left(t_0\right)$ of the four wave packets are shown by the dashed curves with different colors. The arrow in (c) shows the time evolution direction. The laser intensity is $1.4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for 800 nm and $1.4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for 1600 nm and $\mathrm{\Delta }\phi =0$.

Figure 2

The simulated two-dimensional PADs of a hydrogen atom (a) without and (b) with the Coulomb potential by the semiclassical interference model. The bottom panel (c) shows the ab initio TDSE results. The relative phase of the OTC field is labeled at the top of the figure. The field-driven photoelectron momenta $\mathbf{p}=-\mathbf{A}\left(t_0\right)$ of the four wave packets are shown in (a) by the dashed curves with different colors (black for w1, red for w2, gray for w3, and green for w4). The white dashed lines in (b) show the stripelike interference patterns. The laser intensity is $1.4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for 800 nm and $1.4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for 1600 nm.

Figure 3

Subcycle interference of the wave packets at different time scales in the OTC field of $\mathrm{\Delta }\phi =0.25\pi$ [(a) and (b)] and $\mathrm{\Delta }\phi =0.75\pi$ [(c) and (d)]. The top panels of each plot show the 800-nm electric field of the OTC pulse. The bottom panels show the semiclassical simulation that includes the selected wave packets in each cycle of the OTC pulse. The dashed curves show the field-driven photoelectron momenta $\mathbf{p}=-\mathbf{A}\left(t_0\right)$. See text for the definition of the direct trajectory $\mathrm{D}n$ and rescattering trajectory $\mathrm{R}n$ for the four wave packets. The laser intensity is $1.4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for 800 nm and $1.4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ for 1600 nm.