Full experimental determination of tunneling time with attosecond-scale streaking method.

Tunneling is one of the most fundamental and ubiquitous processes in the quantum world. The question of how long a particle takes to tunnel through a potential barrier has sparked a long-standing debate since the early days of quantum mechanics. Here, we propose and demonstrate a novel scheme to accurately determine the tunneling time of an electron. In this scheme, a weak laser field is used to streak the tunneling current produced by a strong elliptically polarized laser field in an attoclock configuration, allowing us to retrieve the tunneling ionization time relative to the field maximum with a precision of a few attoseconds. This overcomes the difficulties in previous attoclock measurements wherein the Coulomb effect on the photoelectron momentum distribution has to be removed with theoretical models and it requires accurate information of the driving laser fields. We demonstrate that the tunneling time of an electron from an atom is close to zero within our experimental accuracy. Our study represents a straightforward approach toward attosecond time-resolved imaging of electron motion in atoms and molecules.

Analyzing the electron trajectories in strong-field tunneling ionization with the phase-of-the-phase spectroscopy.

By numerically solving the time-dependent Schrödinger equation, we theoretically study strong-field tunneling ionization of Ar atom in the parallel two-color field which consists of a strong fundamental pulse and a much weaker second harmonic component. Based on the quantum orbits concept, we analyzed the photoelectron momentum distributions with the phase-of-the-phase spectroscopy, and the relative contributions of the two parts of the photoelectrons produced during the rising and falling edges of the adjacent quarters of the laser cycle are identified successfully. Our results show that the relative contributions of these two parts depend on both of the transverse and longitude momenta. By comparing the results from model atoms with Coulomb potential and short-range potential, the role of the long-range Coulomb interaction on the relative contributions of these two parts of electrons is revealed. Additionally, we show that the effects of Coulomb interaction on ionization time are vital for identifying their relative contributions.

Intensity-dependent angular distribution of low-energy electrons generated by intense high-frequency laser pulse.

By solving the three-dimensional time-dependent Schrödinger equation, we investigate the angular distributions of the low-energy electrons when an intense high-frequency laser pulse is applied to the hydrogen atom. Our numerical results show that the angular distributions of the low-energy electrons which generated by the nonadiabatic transitions sensitively depend on the laser intensity. The angular distributions evolve from a two-lobe to a four-lobe structure as the laser intensity increases. By analyzing nonadiabatic process in the Kramers-Henneberger frame, we illustrate that this phenomenon is attributed to the intensity-dependent adiabatic evolution of the ground state wavefunction. When the laser intensity further increases, the pathway of nonadiabatic transition from the ground state to the excited state and then to the continuum states is non-negligible, which results in the ring-like structure in the photoelectron momentum distribution. The angular distributions of the low-energy electrons provide a way to monitor the evolution of the electron wavefunction in the intense high frequency laser fields.

Low-energy photoelectron interference structure in attosecond streaking.

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.

Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses.

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.

Frustrated tunneling ionization in the elliptically polarized strong laser fields.

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.

Determination of the Ionization Time Using Attosecond Photoelectron Interferometry.

Laser-induced electron tunneling ionization from atoms and molecules plays as the trigger for a broad class of interesting strong-field phenomena in attosecond community. Understanding the time of electron tunneling ionization is vital to achieving the ultimate accuracy in attosecond metrology. We propose a novel attosecond photoelectron interferometer, which is based on the interference of the direct and near-forward rescattering electron wave packets, to determine the time information characterizing the tunneling process. Adding a weak perturbation in orthogonal to the strong fundamental field, the phases of the direct and the near-forward rescattering electron wave packets are modified, leading to the shift of the interferogram in the photoelectron momentum distributions. By analyzing the response of the interferogram to the perturbation, the real part of the ionization time, which denotes the instant when the electron exits the potential barrier, and the associated rescattering time are precisely retrieved. Moreover, the imaginary part of the ionization time, which has been interpreted as a quantity related to electron motion under the potential barrier, is also unambiguously determined.