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Above-threshold ionization (ATI) is one of the most fundamental processess when atoms or molecules are subjected to intense laser fields. Analysis of ATI process in intense laser fields by a Wigner-distribution-like (WDL) function is reviewed in this paper. The WDL function is used to obtain various time-related distributions, such as time-energy distribution, ionization time distribution, and time-emission angle distribution and so on, of atoms in laser field pulses with different laser parameters. For the linearly polarized laser pulses, the time-energy distribution intuitively shows from a quantum point of view the relationship between the ionization moment and the final energy and clearly reveals the origin of interference structures in the photoelectron spectrum. In particular, for linearly polarized few-cycle laser pulses, all calculated distributions show the dependence of electron behavior on the ionization time, emission direction, and carrier-envelope phase (CEP). For elliptically polarized few-cycle pulses, we calculate the angular distribution, ionization time distribution, and time-emission distribution, which are compared with the semiclassical calculations. Analysis shows that the offset angle (difference between positions of the peaks in the angular distributions obtained by two methods) in the angular distributions does not correspond to the offset time (difference between positions of the peaks in the ionization time distributions obtained by two methods) in the ionization time distributions, which implies that the attosecond angular streaking technique based on this correspondence between the offset angle and time is in principle inaccurate. Furthermore, the offset time cannot be interpreted as tunneling time.

Based on the strong-field approximation (SFA), we investigate the interference between different returning orbits of the rescattering electron in nonsequential double ionization. We find that the effect of interference is negligible in the recollision-impact ionization process but is prominent in the recollision excitation with subsequent ionization process and induces fast oscillation with constant period in the laser intensity dependence of the asymmetry parameter. The dominant contribution to the fast oscillation comes from the mixed interference between different pairs of returning orbits in different excitation channels. However, the oscillation disappears after laser focus averaging is performed due to its rather small period.

We use a Wigner distribution-like function based on the strong field approximation theory to obtain the time-energy distributions and the ionization time distributions of electrons ionized by an XUV pulse alone and in the presence of an infrared (IR) pulse. In the case of a single XUV pulse, although the overall shape of the ionization time distribution resembles the XUV-envelope, its detail shows dependence on the emission direction of the electron and the carrier-envelope phase of the pulse, which mainly results from the low-energy interference structure. It is further found that the electron from the counter-rotating term plays an important role in the interference. In the case of the two-color pulse, both the time-energy distributions and the ionization time distributions change with varying IR field. Our analysis demonstrates that the IR field not only modifies the final electron kinetic energy but also changes the electron’s emission time, which is attributed to the change of the electric field induced by the IR pulse. Moreover, the ionization time distributions of the photoelectrons emitted from atoms with higher ionization energy are also given, which show less impact of the IR field on the electron dynamics.

Consensus has been reached that recollision, as the most important post-tunneling process, is responsible for nonsequential double ionization process in intense infrared laser field, however, its effect has been restricted to interaction between the first ionized electron and the residual ion so far. Here we identify the key role of recollision of the second ionized electron, which is enhanced by the stronger Coulomb potential of the higher valence residual ion, in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method, which enables us to well reproduce the experimentally observed cross-shaped and anti-correlated patterns in correlated two-electron momentum distributions, and also the transition between these two patterns. Being significantly enhanced relatively by the recapture process which is also attributed to the stronger Coulomb potential of the residual ion, recolliding trajectories of the second electron excited by the first- or third-return recolliding trajectories of the first electron produce the cross-shaped or anti-correlated distributions, respectively. And the transition is induced by the increasing contribution of the third return with increasing pulse duration. Our work provides a new insight into atomic ionization dynamics and paves the new way to imaging of ultrafast dynamics of atoms and molecules in intense laser field.

The consensus on the mechanism of atomic excitation in an intense laser field has not been reached so far because the proposed mechanisms may dominate in different regimes. In this paper, we show a clear transition of the underlying physical mechanism of strong-field atomic excitation from multiphoton resonance to coherent recapture by investigating the intensity dependence of the yields of neutral excited atoms $({\mathrm{Ar}}^{*})$ and singly charged ions $({\mathrm{Ar}}^{+})$ of argon experimentally and theoretically. Our results indicate that, for 400 nm, the multiphoton resonance mechanism plays a significant role at low intensity and coherent recapture mechanism becomes important at high intensity. While for 800 nm, distinctive out-of-phase oscillations of ${\mathrm{Ar}}^{*}$ and ${\mathrm{Ar}}^{+}$ yields are identified, implying that coherent recapture mechanism dominates. Our work provides a more comprehensive understanding of the atomic excitation mechanism in an intense laser field.

We have performed a comparison study of the Rydberg-state excitation of model molecules (1π g and 1π u states) in different laser fields by the approaches of time-dependent Schrödinger equation and a fully quantum-mechanical model, and both simulations show good accordance. It is found that the peak structure of the Rydberg-state population vs laser intensity becomes pronounced for longer laser pulses due to the stronger interference effect between the subwave packets released in different optical cycles, and the locations of the intensity-dependent peaks closely satisfy the multi-photon resonant transition condition. In addition, it is demonstrated that the populations of the Rydberg states possessing the identical parity oscillate in an inverse manner with increasing laser intensity for different initial states (1π g and 1π u ), and the aforementioned distinct phenomenon is attributed to the additional phase introduced by the symmetry of 1π g state with respect to that of 1π u state.

A Wigner distributionlike function based on the improved strong-field approximation theory is proposed to calculate the rescattering time-energy distribution (RTED) of high-energy photoelectrons of atomic above-threshold ionization process in few-cycle laser fields with different frequencies. The RTED shows bell-like stripes and the outermost stripe is compared with semiclassical results given by the simple-man model with consideration of different positions of tunnel exit and different initial longitudinal momenta. Analysis indicates the existence of the tunnel exit. However, though it shifts farther away from the core with decreasing frequency, the position of the tunnel exit is significantly less than the prediction by adiabatic theory even for the low-frequency case which is well in the tunneling regime. Our results also imply that the effect of the tunnel exit is more important than that of the initial longitudinal momentum at the tunnel exit for the backward-scattering electrons. Moreover, the inner stripe structures in the RTED are attributed to interference between electrons with the same final energy emitted at different ionization times.

We investigate the ionization dynamics of one-electron model diatomic molecules with different orbital symmetries ($1{\ensuremath{\sigma}}_{g}$ and $1{\ensuremath{\sigma}}_{u}$) in a strong laser field via the full three-dimensional time-dependent Schr\"odinger equation. It is shown that the ionization probabilities of the molecules with different initial states ($1{\ensuremath{\sigma}}_{g}$ and $1{\ensuremath{\sigma}}_{u}$) oscillate out of phase vs internuclear distance, and the photoelectron spectra of the aforementioned two molecules also show out-of-phase oscillation structures. The above intriguing features are well reproduced by the simulations of the length-gauge strong-field approximation, which can be ascribed to the distinct interferences of electronic wave packets released from different atomic centers.

Strong-field ionization and Rydberg-state excitation (RSE) near the continuum threshold exhibit two phenomena that have attracted a lot of recent attention: the low-energy structure (LES) just above and frustrated tunneling ionization just below the threshold. The former becomes apparent for longer laser wavelengths, while the latter has been especially investigated in the near infrared; both have been treated as separate phenomena so far. Here we present a unified perspective based on electron trajectories, which emphasizes the very important role of the electron-ion Coulomb interaction as expected in this energy region. Namely, those trajectories that generate the LES can also be recaptured into a Rydberg state. The coherent superposition of the contributions of such trajectories with different travel times (each generating one of the various LES peaks) causes an oscillation in the intensity dependence of the RSE yield, which is especially noticeable for longer wavelengths. The theory is illustrated by RSE experiments at 1800 nm, which agree very well with the theory with respect to position and period of the oscillation. The wavelength scaling of the RSE oscillation is also discussed. Our work establishes a solid relationship between processes below and above the threshold and sheds new light on atomic dynamics driven by intense laser fields in this critical energy region.

We have studied ionization and excitation of model molecules possessing different initial states (1sσ g and 1sσ u ) in 800 nm laser pulses by numerical solution of three-dimensional time-dependent Schrödinger equation and quantum models. Calculations of two methods show good agreement. It is found that the locations of the peaks of total Rydberg-state probability vs laser intensity do not coincide for different initial states, which is ascribed to the fact that the relative contributions from Rydberg states change due to the difference of the ionization time distributions for different initial states induced by the two-center interference effect. In addition, it is demonstrated that the suppression of ionization is more obvious than that of excitation compared the results of 1sσ u state with those of 1sσ g state, which is attributed to the distinct interference effects for molecular ionization and excitation in strong laser fields.

Quantum interference plays an important role in various intense-laser-driven atomic phenomena, e.g., above-threshold ionization and high-order-harmonic generation, and provides a useful tool in ultrafast imaging of atomic and molecular structure and dynamics. However, it has eluded observation in nonsequential double ionization (NSDI), which serves as an ideal prototype to study electron-electron correlation. Thus far, NSDI usually could be well understood from a semiclassical perspective, where all quantum aspects have been ignored after the first electron has tunneled. Here we perform coincidence measurements for NSDI of xenon subject to laser pulses at 2400 nm. It is found that the intensity dependence of the asymmetry parameter between the yields in the second and fourth quadrants and those in the first and third quadrants of the electron-momentum-correlation distributions exhibits a peculiar fast oscillatory structure, which is beyond the scope of the semiclassical picture. Our theoretical analysis indicates that this oscillation can be attributed to interference between the contributions of different excited states in the recollision-excitation-with-subsequent-ionization channel. Our work demonstrates the significant role of quantum interference in NSDI and may create an additional pathway towards manipulation and imaging of the ultrafast atomic and molecular dynamics in intense laser fields.

We experimentally investigate the recoil-ion momentum distribution along the laser polarization direction for nonsequential double ionization of Xe by 50 fs, 2400 nm laser pulses at intensities of $(22\ensuremath{-}68) \mathrm{TW}/{\mathrm{cm}}^{2}$. The observed doubly charged ion momentum distribution exhibits a distinct transition from a flat-top structure near zero longitudinal momentum at $22\phantom{\rule{0.16em}{0ex}}\mathrm{TW}/{\mathrm{cm}}^{2}$ to the one with two maxima at nonzero longitudinal momentum at $37\phantom{\rule{0.16em}{0ex}}\mathrm{TW}/{\mathrm{cm}}^{2},\phantom{\rule{4pt}{0ex}}52\phantom{\rule{0.16em}{0ex}}\mathrm{TW}/{\mathrm{cm}}^{2}$, and $68\phantom{\rule{0.16em}{0ex}}\mathrm{TW}/{\mathrm{cm}}^{2}$, which is remarkably different from the case of 800 nm. Simulation based on a semiclassical model is used to obtain the ratios of contributions from the recollision-impact ionization (RII) and the recollision-induced excitation with subsequent field ionization (RESI) in nonsequential double ionization. Our calculation reveals that the increasing contribution of the RII channel is responsible for the more prominent double-hump structure at longer wavelength or higher laser intensity. Moreover, a simple fitting based on the calculated ratios allows one to reproduce the experimental ion momentum distributions well and obtain contributions from these two channels.

We introduce an ab initio approach and the modified strong-field approximation to investigate the alignment-dependent ionization of H2+(1πu) exposed to different few-cycle laser fields. The ab initio calculations are performed by the B-splines one-center method and the Crank-Nicolson method in spherical coordinates. It is shown that the peak ionization probabilities appear around alignment angles 50° and 40° at the laser intensities 3×1013 W/cm2 and 5×1013 W/cm2, respectively, and the above distinct features come from the resonant excitation of the molecular ion, which is confirmed by calculation including and excluding the state 2σg in the basis expansion. Furthermore, the results obtained by including the state 2σg in the ab initio simulations can be qualitatively reproduced by the modified molecular length gauge strong-field approximation (SFA) taking account of the 1πu and 2σg states simultaneously. Analysis indicates that a part of electron is directly emitted from the 1πu orbital and another portion of electron is released from 2σg orbital and other excited state after the single-photon resonant transition between 1πu and 2σg orbitals.