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By numerically solving the time-dependent Schrödinger equation, we theoretically investigate the dynamics of the low-energy photoelectrons ionized by a single attosecond pulse in the presence of an infrared laser field. The obtained photoelectron momentum distributions exhibit complicated interference structures. With the semiclassical model, the originations for the different types of the interference structures are unambiguously identified. Moreover, by changing the time delay between the attosecond pulse and the infrared laser field, these interferences could be selectively enhanced or suppressed. This enables us to extract information about the ionization dynamics encoded in the interference structures. As an example, we show that the phase of the electron wave-packets ionized by the linearly and circularly polarized attosecond pulses can be extracted from the interference structures of the direct and the near-forward rescattering electrons.

Strong-field photoelectron holography (SFPH), originating from the interference of the direct electron and the rescattering electron in tunneling ionization, is a significant tool for probing structure and electronic dynamics in molecules. We theoretically study SFPH by counter rotating two-color circularly (CRTC) polarized laser pulses. Different from the case of the linearly polarized laser field, where the holographic structure in the photoelectron momentum distribution (PEMD) is clustered around the laser polarization direction, in the CRTC laser fields, the tunneling ionized electrons could recollide with the parent ion from different angles and thus the photoelectron hologram appears in the whole plane of laser polarization. This property enables structural information delivered by the electrons scattering the molecule from different angles to be recorded in the two-dimensional photoelectron hologram. Moreover, the electrons tunneling at different laser cycles are streaked to different angles in the two-dimensional polarization plane. This property enables us to probe the sub-cycle electronic dynamics in molecules over a long time window with the multiple-cycle CRTC laser pulses.

We theoretically investigated frustrated tunneling ionization (FTI) in the interaction of atoms with elliptically polarized laser pulses by a semiclassical ensemble model. Our results show that the yield of frustrated tunneling ionization events exhibits an anomalous behavior which maximizes at the nonzero ellipticity. By tracing back the initial tunneling coordinates, we show that this anomalous behavior is due to the fact that the initial transverse velocity at tunneling of the FTI events is nonzero in the linear laser pulses and it moves across zero as the ellipticity increases. The FTI yield maximizes at the ellipticity when the initial transverse momentum for being trapped is zero. Moreover, the angular momentum distribution of the FTI events and its ellipticity dependence are also explored. The anomalous behavior revealed in our work is very similar to the previously observed ellipticity dependence of the near- and below-threshold harmonics, and thus our work may uncover the mechanism of the below-threshold harmonics which is still a controversial issue.

Using the classical ensemble method, we have investigated the alignment dependence of the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of diatomic molecules driven by linearly polarized laser pulses. Our numerical results show that the correlated electron pairs are more likely to emit into the same hemisphere (side-by-side emission) for the parallel aligned molecules at the small internuclear distance, in agreement with previous experimental results. Surprisingly, as the internuclear distance increases, this side-by-side emission is more prevalent for the perpendicularly aligned molecules. Back analyzing of the classical trajectories shows that a considerable part of the NSDI events for the parallel aligned molecules at the large internuclear distances occur through an internal collision, not the well-known recollision. In the internal collision induced NSDI, the first electron tunnels through the inner barrier from the up-field core, moves directly towards the other core, and kicks out the second electron. For this type of NSDI events, the electron pairs are more likely to emit into the opposite hemispheres and thus the correlated electron momentum spectrum exhibits a more dominant back-to-back behavior in the parallel aligned molecules.

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

With the semiclassical ensemble model, we systematically investigate the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) by the counter-rotating circularly polarized two-color (CPTC) laser pulses. Our results show that the angular distributions of the electrons in NSDI sensitively depend on the intensity ratio of the CPTC laser fields. At the small ratio, the electron pairs emit with a relative angle of about 120°, and this angle shifts to 40° as the ratio increases and finally it exhibits a wide range distribution as the intensity ratio further increases. Back analysis of the NSDI trajectories shows that this behavior results from the relative-intensity-dependence of the release time of the electron pairs in the CPTC laser fields. The release times of the electron pairs are directly mapped to the angular distribution. Our results indicate that the emission times of the correlated electrons in NSDI can be controlled with the CPTC laser fields.

Electron correlation is ubiquitous across diverse physical systems from atoms and molecules to condensed matter. Observing and controlling dynamical electron correlation in photoinduced processes paves the way to the coherent control of chemical reactionsand photobiological processes. Here, we experimentally investigate dynamics of electron correlation in double ionization of neon irradiated by intense elliptically polarized laser pulses. We find a characteristic, ellipticity-dependent, correlated electron emission along the minor axis of the elliptically polarized light. This observation is well reproduced by a semi-classical ensemble model simulation. By tracing back the corresponding electron trajectories, we find that the dynamical energy sharing during the electron emission process is modified by the ellipticity of the laser light. Thus, our work provides evidence for a possible ultrafast control of the energy sharing between the correlated electrons by varying the light ellipticity.

Accurate determination of laser intensity is of fundamental importance to study various phenomena in intense laser-atom/molecule interactions. We theoretically demonstrate a scheme to measure laser intensity by examining the holographic structure originating from the interference between the direct and near-forward rescattering electrons in strong-field tunneling ionization. By adding a weak second-harmonic field with polarization orthogonal to the strong fundamental driving field, the interference pattern oscillates with the changing relative phases of the two-color fields. Interestingly, the amplitude of this oscillation in the photoelectron momentum spectrum depends on the parallel momentum. With the quantum-orbit analysis, we show that the amplitude of the oscillation minimizes when the time difference between the recollision and ionization of near-forward rescattering electron is half cycle of the fundamental driving field. This enables us to measure accurately the laser intensity by seeking the minimum of the oscillation amplitude. Moreover, we show that this minimum can be determined without scanning the relative phases, instead, by just monitoring the interference patterns for two relative phases. This facilitates the application of our scheme in experiment.

We report on the scaling of the photoelectron holography with the laser ellipticity in strong-field atomic ionization. We find that the spacing of the holographic fringe gradually decreases with increasing of the ellipticity. In terms of the strong-field approximation, the scaling of the fringe spacing with the laser ellipticity is explained by the effect of the initial transverse momenta at the tunnel exit. With increasing of the laser ellipticity, a ridge structure arising from forward scattering electrons is observed in the low-energy region of the electron momentum distribution. An analytic formula is obtained that demarcates the phase diagram for the observation of the holographic pattern and ridge structure in elliptically polarized laser fields.

We measure the recoil-ion momentum distributions from nonsequential double ionization of Ne by two-color laser pulses consisting of a strong 800-nm field and a weak 400-nm field with parallel polarizations. The ion momentum spectra show pronounced asymmetries in the emission direction, which depend sensitively on the relative phase of the two-color components. Moreover, the peak of the doubly charged ion momentum distribution shifts gradually with the relative phase. The shifted range is much larger than the maximal vector potential of the 400-nm laser field. Those features are well recaptured by a semiclassical model. Through analyzing the correlated electron dynamics, we found that the energy sharing between the two electrons is extremely unequal at the instant of recollison. We further show that the shift of the ion momentum corresponds to the change of the recollision time in the two-color laser field. By tuning the relative phase of the two-color components, the recollision time is controlled with attosecond precision.

We study the carrier-envelope phase (CEP) dependent photoelectron energy spectra from above-threshold ionization by numerically solving the time-dependent Schrödinger equation of hydrogen atom in a few-cycle laser field at intensities in the range of (2-10) × 10 13 W/cm 2 . Depending on the electron energy and the laser intensity, the yield of the photoelectron reveals clear oscillations with respect to the CEP. At high laser intensities (larger than ~3 × 10 13 W/cm 2 ), the yield of the high-energy photoelectrons (larger than 2U p , with U p being the ponderomotive potential) shows two kinds of oscillations with the CEP for different electron energies. There is a clear phase jump for those two kinds of oscillations. In contrast, at low laser intensities (smaller than ~3 × 10 13 W/cm 2 ), the phase of the oscillation for the high-energy photoelectron yield with the CEP is nearly independent on the electron energy, which will reduce the sensitivity of the retrieval of single-shot CEP using the method reported by T. Wittmann et al. [Nat. Phys. 5, 357 (2009)] at low laser intensities. We further show that the low-energy photoelectrons display distinct CEP-dependent intercycle interference fringes, providing an alternative approach to retrieve the CEP with high sensitivity in a few-cycle laser field with low intensity.

Recent experiments on strong-field sequential double ionization (SDI) have reported several observations which are regarded as evidence of electron correlation, querying the validity of the standard independent electron approximation for SDI. Here we theoretically study SDI with a classical ensemble model. The experimental results are well reproduced with this model. Back tracing of the ionization process shows that these results are ascribed to the subcycle ionization dynamics of the two electrons, not the evidences of the electron correlation in SDI. Thus, the previously reported observations are not enough to claim the breakdown of the independent electron approximation in SDI.

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

Backscattering photoelectron hologram (BPH) originating from direct and backward-rescattering electrons encodes important structural information and ultrafast dynamics of the underlying processes. However, the BPH is usually overshadowed by other interference structures in the photoelectrons momentum spectra, preventing a direct extraction of information using BPH. Here we theoretically demonstrate disentanglement of the BPH from other types of interference with the orthogonal two-color field, where a weak orthogonal component is used to streak the BPH. By carefully adjusting the relative phase of the two-color field, the BPH is effectively separated from other interferences in the photoelectron momentum spectra and thus the BPH is unambiguously identified. This takes a significant step to time-resolved imaging of the attosecond dynamics with strong-field photoelectron holography.

Using a fully classical model, we have studied sequential double ionization (SDI) of argon driven by elliptically polarized laser pulses at intensities well in the over-barrier ionization region. The results show that ion momentum distributions evolve from the two-band structure to the four-band, six-band structure and finally to the previously obtained four-band structure as the pulse duration increases. Our analysis shows that the evolution of these band structures originates from the pulse-duration-dependent multiple ionization bursts of the second electron. These band structures unambiguously indicate the subcycle electron emission in SDI.

The multielectron dynamics in nonsequential triple ionization (NSTI) of neon atoms driven by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. In consistent with the experimental result, our numerical result shows that in the MIR regime, the triply charged ion longitudinal momentum spectrum exhibits a pronounced double-hump structure at low laser intensity. Back analysis reveals that as the intensity increases, the responsible triple ionization channels transform from direct (e, 3e) channel to the various mixed channels. This transformation of the NSTI channels leads to the results that the shape of ion momentum spectra becomes narrow and the distinct maxima shift towards low momenta with the increase of the laser intensity. By tracing the triply ionized trajectories, the various ionization channels at different laser intensities are clearly identified and these results provide an insight into the complex dynamics of the correlated three electrons in NSTI.

With the three-dimensional classical ensemble model, we investigate the correlated electron emission in nonsequential double ionization (NSDI) of argon atoms by few-cycle laser pulses. Our calculations well reproduce the experimentally observed cross-shaped structure in the correlated two-electron momentum spectrum [ Nature Commun. 3, 813 (2012)]. By tracing these NSDI trajectories, we find that besides the process of recollision-induced excitation with subsequent ionization just before the next field maximum, the recollision ionization also significantly contributes to the cross-shaped structure.

We theoretically investigated sequential double ionization (SDI) of Ar by the nearly circularly polarized laser pulses with a fully correlated classical ensemble model. The ion momentum distributions of our numerical results at various laser intensities and pulse durations agree well with the experimental results. The experimentally observed multi-electron effects embodied in the joint momentum spectrum of the two electrons is also reproduced by our correlated classical calculations. Interestingly, our calculations show that the angular distribution of the first photoelectron from the trajectories which eventually suffer SDI differs from the distribution of the photoelectrons from above-threshold ionization trajectories. This observation provides additional evidence of multi-electron effects in strong field SDI.

The electron dynamics in strong field nonsequential double ionization (NSDI) of nitrogen molecules by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. The numerical results show that in the MIR regime, the correlated behavior of the two electrons from NSDI is independent on the molecular alignment, contrary to the case in the near-infrared (NIR) regime where the electron correlations exhibit a strong alignment dependence. In consistent with the experimental results, our numerical results show that the longitudinal momentum spectrum of the doubly charged ion evolves from a wide single-hump structure at NIR regime into a double-hump structure when wavelength enters the MIR regime. This double-hump structure becomes more pronounced as the wavelength further increases. The responsible microscopic electron dynamics of NSDI at the MIR regime is explored by back analysis of the classical trajectories.

With the classical fermion molecular dynamics model (FMD), we investigated electron emissions from H(2)(+) by circularly polarized laser pulses. The obtained electron momentum distribution clearly shows an angular shift relative to the expected direction for H(2)(+) aligned parallel to the polarization plane, which is in good agreement with the recent experimental result. By tracing the classical trajectory, we provide direct evidence for the electron delayed emission with respect to the instant when the electric field is parallel to the molecular axis, which was regarded as the origin of the angular shift in the electron momentum distribution. Furthermore, we find that the angular shift decreases with increasing the laser wavelength.

Ionization of molecules by strong laser fields launches an electron wave packet. This electron wave packet, which can be driven back by the field to recollide with the parent ion, has been widely explored to probe the ultrafast nuclear dynamics. We numerically demonstrate the precise control of the temporal characteristic of the recolliding electron wave packet (REWP) by orthogonally polarized two-color fields. Through changing the relative phase of the two fields, the revisit time of REWP can be manipulated with a resolution of less than 200 attos, thus significantly improving the resolution of the well known molecular clock. This provides an efficient method for real-time observation of the ultrafast molecular dynamics with attosecond resolution., (© 2011 Optical Society of America)

The electron-electron correlation in nonsequential double ionization (NSDI) from aligned molecules by linearly polarized 800 nm laser pulses has been investigated with the three-dimensional classical ensemble model. The result shows that for the perpendicular alignment the two electrons involved in NSDI more likely exit the molecule into the opposite hemispheres as compared to the parallel alignment, which agrees well with the experimental result [Phys. Rev. Lett. 95, 203003 (2005)]. This alignment effect is qualitatively explained based on the suppressed potential barriers which are different for parallel molecules and perpendicular molecules. Additionally, the intensity dependence of the alignment effect is also explored.

We have investigated the correlated electron dynamics in nonsequential double ionization (NSDI) of helium by the orthogonally polarized two-color pulses that consisted of an 800-nm and a 400-nm laser fields using the classical ensemble model. Depending on the relative phase of the two-color field, the electron momentum distributions along the polarization direction of the 800-nm field exhibit a surprisingly strong anticorrelated or correlated behavior. Back analysis reveals that recollisions eventually leading to NSDI are concentrated in a time window as short as several hundreds attoseconds with this scheme. By changing the relative phase of the two-color field, the revisit time of recolliding electron wave packet has been controlled with attosecond precision, which is responsible for the various correlated behaviors of the two electrons. Our results reveal that the orthogonally polarized two-color field can serve as a powerful tool to control the correlated electron dynamics in NSDI.

Using the full three-dimensional classical ensemble model, we have investigated nonsequential triple ionization (NSTI) of Ne by intense linearly polarized laser fields systematically. Trajectory back analysis enables us to identify the various NSTI channels at different intensities in an intuitive way. The momentum distributions of the triply ionized ions calculated by this model agree well with the experimental results over a wide range of laser intensities [J. Phys. B 41, 081006 (2008)]. With this classical model we achieve insight into the complex sub-laser-cycle dynamics of the correlated three electrons in NSTI.

We have investigated the 2D photoelectron momentum spectra for ATI of atoms exposed to linearly polarized pulses by quantum mechanical calculations. By comparing the 2D momentum spectra for the long-range and short-range Coulomb potentials, the focusing of the electron transverse momentum by the long-range interaction is clearly revealed. Analysis indicates that the Coulomb attraction of the parent core to the returning electron is responsible for the focusing of the electron transverse momentum. Moreover, the strong dependence of the focusing of the electron transverse momentum on the laser wavelength and intensity is discussed.

Using three-dimensional classical ensembles, we have investigated the internuclear distance dependence of nonsequential double ionization (NSDI) of H(2) molecules by an 800 nm, 1x10(14) W/cm(2) laser pulse. For the internuclear distance R ranging from 2 to 12 a.u., the NSDI of H(2) provides rich correlation patterns in the two-electron momentum distributions. These correlation patterns essentially reveal different microscopic dynamics in NSDI process. Moreover, our calculations show that R approximately 4 a.u. is the critical distance for double ionization yield of H(2). These results are qualitatively explained based on the classical barrier expression model and back analysis.

Using the classical three-dimensional ensembles, we have demonstrated the controlling of dynamics in nonsequential double ionization (NSDI) of helium by two-color few-cycle pulses. By changing the relative phase of the two pulses, recollisions leading to NSDI can be restricted in a time interval of several hundreds attosecond nearly before the field extremum and as a result, the correlated electron momentum distribution exhibits a so-far unobserved narrow arc-like structure. This structure reveals a novel energy correlation between the two electrons from NSDI by two-color few-cycle pulses.