Taking snapshots of a moving electron wave packet in molecules using photoelectron holography in strong-field tunneling ionization

Coherent superposition of electronic states induces attosecond electron motion in molecules.We theoretically investigate the strong-field ionization of this superposition state by numerically solving the time-dependent Schrodinger equation.In the obtained photoelectron momentum distribution,an intriguing bifurcation structure appears in the strong-field holographic interference pattern.We demonstrate that this bifurcation structure directly provides complete information about the status of the transient wave function of the superposition state:the horizontal location of the bifurcation in the momentum distribution reveals the relative phase of the involved components of the superposition state and the vertical position indicates the relative coefficient.Thus,this bifurcation structure takes a snapshot of the transient electron wave packet of the superposition state and provides an intuitive way to monitor electron motion in molecules.

Backward rescattered photoelectron holography in strong-field ionization

By numerically solving the time-dependent Schr¨odinger equation, we observe a remarkable strong-field interference pattern in the photoelectron momentum distribution of a hydrogen atom ionized by a few-cycles laser pulse. This interference pattern is joined together with the familiar near-forward strong-field photoelectron holographic interference. By applying the strong-field approximation theory, we investigate the formation of this interference pattern, which arises from the interference between the backward rescattered part and the direct part of the tunneling ionized electron wave packet. We demonstrate that this backward rescattered photoelectron holographic interference can also be observed in a more realistic parallel two-color laser field. These results pave a new way to look into the atomic and molecular structure with ultrafast timescale.

Scattering-amplitude phase in spiderlike photoelectron momentum distributions

The spiderlike structures in the photoelectron momentum distributions of ionized electrons from the hydrogen atom are numerically simulated by using a semiclassical rescattering model(SRM) and solving the time-dependent Schrodinger equation(TDSE),focusing on the role of the phase of the scattering amplitude.With the SRM,we find that the spiderlike legs shift to positions with smaller transverse momentum values while increasing the phase.The spiderlike patterns obtained by SRM and TDSE are in good agreement upon considering this phase.In addition,the time differences in electron ionization and rescattering calculated by SRM and the saddle-point equations are either in agreement or show very similar laws of variation,which further corroborates the significance of the phase of the scattering amplitude.

Resolving and weighing the quantum orbits in strong-field tunneling ionization

Tunneling ionization of atoms and molecules induced by intense laser pulses contains the contributions of numerous quantum orbits.Identifying the contributions of these orbits is crucial for exploring the application of tunneling and for understanding various tunneling-triggered strong-field phenomena.We perform a combined experimental and theoretical study to identify the relative contributions of the quantum orbits corresponding to the electrons tunneling ionized during the adjacent rising and falling quarter cycles of the electric field of the laser pulse.In our scheme,a perturbative second-harmonic field is added to the fundamental driving field.By analyzing the relative phase dependence of the signal in the photoelectron momentum distribution,the relative contributions of these two orbits are unambiguously determined.Our results show that their relative contributions sensitively depend on the longitudinal momentum and modulate with the transverse momentum of the photoelectron,which is attributed to the interference of the electron wave packets of the long orbit.The relative contributions of these orbits resolved here are important for the application of strong-field tunneling ionization as a photoelectron spectroscopy for attosecond time-resolved measurements.

Probing the launching position of the electron wave packet in molecule strong-field tunneling ionization

Strong-field tunneling ionization is the first step for a broad class of phenomena in intense laser-atom/molecule interactions. Accurate information about the electron wave packet from strong-field tunneling ionization of atoms and molecules is of essential importance for understanding various tunneling ionization triggered processes. Here, we survey the property of the electron wave packet in tunneling ionization of molecules with a method based on strong-field photoelectron holography. By solving the time-dependent Schr ¨odinger equation, it is shown that the holographic interference in the photoelectron momentum distribution exhibits the asymmetric behavior with respect to the laser polarization direction, when the molecule is aligned with a nonzero angle to the linearly polarized laser field. We demonstrate that this asymmetry is due to the nonzero initial transverse displacement of the electron wave packet at tunneling. By analyzing the holographic interference, this transverse displacement for the launching of electron wave packet tunneling from the molecules is accurately retrieved. This displacement is directly related to the electron density distribution in molecules, and thus our work developed a novel concept for probing electronic structure in molecules.