Time-resolved photoelectron holography from atoms using midinfrared laser pulses is investigated by solving the corresponding time-dependent Schr\"odinger equation (TDSE) and a classical model, respectively. The numerical simulation of the photoelectron angular distribution of Xe irradiated with a low-frequency free-electron laser source agrees well with the experimental results. Different types of subcycle interferometric structures are predicted by the classical model. Furthermore with the TDSE model it is demonstrated that the holographic pattern is sensitive to the shape of the atomic orbitals. This is a step toward imaging by means of photoelectron holography.

Multichannel molecular high-order harmonic generation (MHOHG) from a single electron asymmetric molecular ion HeH2+ is investigated numerically. It is found that considerable resonant excitation occurs by laser induced electron transfer (LIET) to neighboring ions and multiple frequency (fractional-order) harmonics are observed from the excited states shifted by some energy $\Delta${} from the main N$\omega${} energy harmonics. A time series analysis is used to confirm this MHOHG channel which is created by initial ionization from the excited state prepared by LIET and recombination to the neighboring ion at specific field phases, resulting in interference between recombination pathways from ground and excited states.

Dynamic imaging of the molecular structure of H2+ is investigated by attosecond photoelectron holography. The interference between direct (reference) and backward rescattered (signal) photoelectrons in attosecond photoelectron holography reveals the birth time of both channels and the spatial information of molecular structure. This is confirmed by simulations with a semiclassical model and numerical solutions of the corresponding time-dependent Schr\"odinger equation, suggesting an attosecond time-resolved way of imaging molecular structure obtained from laser induced rescattering of ionized electrons. It is shown that both short and long rescattered electron trajectories can be imaged from the momentum distribution.

Molecular high-order harmonic generation (MHOHG) in a non-Born-Oppenheimer treatment of ${{\mathrm{H}}_2}^{+}$, ${{\mathrm{D}}_2}^{+}$, is investigated by numerical simulations of the corresponding time-dependent Schrödinger equations in full dimensions. As opposed to previous studies on amplitude modulation of intracycle dynamics in MHOHG, we demonstrate redshifts as frequency modulation (FM) of intercycle dynamics in MHOHG. The FM is induced by nuclear motion using intense laser pulses. Compared to fixed-nuclei approximations, the intensity of MHOHG is much higher due to the dependence of enhanced ionization on the internuclear distance. The width and symmetry of the spectrum of each harmonic in MHOHG encode rich information on the dissociation process of molecules at the rising and falling parts of the laser pulses, which can be used to retrieve the nuclear dynamics. Isotope effects are studied to confirm the FM mechanism.

We investigate the high-order-harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schrödinger equations (TDSEs) are solved numerically by using $B$-spline basis sets in coordinate space. The energy-band structure and wave vectors can be directly retrieved from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$-space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly with the field strength. We also study HHG driven by intense few-cycle laser pulses and find that the cutoff energy of the harmonic spectrum is sensitive to the changes of the carrier envelope phase.

Molecules constituted by different isotopes are different in vibrational modes, making it possible to elucidate the mechanism of a chemical reaction via the kinetic isotope effect. However, the real-time observation of the vibrational motion of isotopic nuclei in molecules is still challenging due to its ultrashort time scale. Here we demonstrate a method to monitor the nuclear vibration of isotopic molecules with the frequency modulation of high-order harmonic generation (HHG) during the laser-molecule interaction. In the proof-of-principle experiment, we report a red shift in HHG from H₂ and D₂. The red shift is ascribed to dominant HHG from the stretched isotopic molecules at the trailing edge of the laser pulse. By utilizing the observed frequency shift, the laser-driven nuclear vibrations of H₂ and D₂ are retrieved. These findings pave an accessible route toward monitoring the ultrafast nuclear dynamics and even tracing a chemical reaction in real time.