Strong-field tunneling ionization is the initial step for various ultrafast dynamics in intense laser-atom and/or molecule interactions. Time-resolving tunneling ionization is of crucial importance for accurately understanding these ultrafast processes. In our previous work [Phys. Rev. Lett. 121, 253203 (2018).], we proposed an attosecond photoelectron interferometer based on strong-field photoelectron holography to resolve the tunneling ionization. Here, we show more details about how the complex ionization time of tunneling is retrieved with our scheme. We demonstrate that the Coulomb interaction, which is a tedious and complex problem in dealing with photoelectron interference in strong-field ionization, can be safely canceled in our scheme. This is further confirmed by performing our scheme for both the model atoms with short-range and Coulomb potentials. Additionally, the validity and accuracy of our scheme are confirmed by its application in different targets and different laser parameters. Our scheme provides a reliable and versatile method to resolve the time information of strong-field tunneling ionization.
Strong-field tunneling ionization is the initial step for various ultrafast dynamics in intense laser-atom and/or molecule interactions. Time-resolving tunneling ionization is of crucial importance for accurately understanding these ultrafast processes. In our previous work [Phys. Rev. Lett. 121, 253203 (2018).], we proposed an attosecond photoelectron interferometer based on strong-field photoelectron holography to resolve the tunneling ionization. Here, we show more details about how the complex ionization time of tunneling is retrieved with our scheme. We demonstrate that the Coulomb interaction, which is a tedious and complex problem in dealing with photoelectron interference in strong-field ionization, can be safely canceled in our scheme. This is further confirmed by performing our scheme for both the model atoms with short-range and Coulomb potentials. Additionally, the validity and accuracy of our scheme are confirmed by its application in different targets and different laser parameters. Our scheme provides a reliable and versatile method to resolve the time information of strong-field tunneling ionization.
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.
Photoelectron holography in strong-field tunneling ionization is an efficient way to probe the structures and the ultrafast dynamics information of atoms and molecules. Manipulating the process of photoelectron holography is important for its application. Here, we study theoretically strong-field photoelectron holography in the spatially inhomogeneous field by solving the time-dependent Schr\"odinger equation. Our results show that the returning energy of the rescattering electron is greatly enhanced in the spatially inhomogeneous field, and the holographic interference pattern can be separated from other types of interference in the photoelectron momentum distribution. Moreover, our results show that the time window of tunneling ionization wherein the electron could be driven back to induce holography is broadened in the inhomogeneous field. These properties are beneficial for the application of photoelectron holography in probing the atomic and molecular structures and dynamics. The origin for these properties is analyzed with the classical trajectory model.
Laser-induced tunneling ionization triggers a broad class of strong-field phenomena in the attosecond community. The understanding and application of these ultrafast phenomena require accurate knowledge of the position information for the tunneling electron wave packet (EWP). Here, with strong-field photoelectron holography, we theoretically demonstrate a scheme to retrieve the position of the EWP emitted from molecules in the direction perpendicular to the tunnel. In our scheme, the photoelectron momentum distributions from strong-field tunneling ionization are obtained by solving the time-dependent Schr\"odinger equation. When the molecule is aligned with a nonzero angle to the linearly polarized laser field, a distinct shift of the holographic pattern in the photoelectron momentum distribution is observed. With the quantum-orbit model, we demonstrate that the shift of the holographic pattern is caused by a nonzero initial transverse position of the EWP immediately after tunneling. By tracing their exact correspondence and examining the shift of the holographic pattern, the transverse emission position of the tunnel-ionized EWP is probed accurately. Furthermore, we demonstrate that the complex Coulomb interaction can be safely canceled in our scheme by performing the scheme for both of the model molecules with the short-range and Coulomb potentials. The validity and accuracy of our scheme are confirmed by its application to different molecules, alignments, and laser parameters.
The response time of the electron to light in photoemission is difficult to define and measure. The tunneling ionization of atoms and molecules in a strong laser field is a type of strong field-induced photoelectric effect. In this process, the electron response time will change the time of high-order harmonic generation (HHG), which will have a fundamental influence on the reconstruction of electron attosecond dynamics through HHG. We propose a simple theory to resolve the response time problem in strong field atomic tunneling ionization. The response time corresponds to the strong interaction time of three bodies i.e. Coulomb, electron and laser field, which can be determined at the quantum-classical boundary. The observable directly obtained through response time can quantitatively reproduce a series of attoclock experimental curves and provide consistent explanations for these experimental phenomena. This work introduces the main conclusions of response time theory and summarizes in detail the research progress of this theory. Firstly, this theory can be applied to the orthogonal two-color laser field to quantitatively explain the main characteristic structures of photoelectron momentum distribution (PMD). Besides, with this response time theory, the scaling law of the observable in attoclock experiment can be obtained. The proposal of scaling law is expected to provide a systematical theoretical guide for better understanding the applicability or feasibility of the attoclock under different conditions. In addition, based on the atomic response time theory, we further consider the property of multi-center Coulomb potential of molecular and develop a response time theory suitable for molecular system. Subsequently, we further apply the response time theory to polar molecules, by utilizing the asymmetry of PMD closely related to response time to recognize the permanent dipole (PD) effect within the laser sub-cycle. In the end, we discuss the prospects for research on response time. Firstly, it is envisioned to further apply response time theory to weak light and single photon transition to detect the response time of related processes. Besides, considering the significant influence of response time on the property of time-domain of HHG electron trajectories, the recombination (re-scattering) effect based on the current strong field tunneling ionization response time theory can be further investigated, thus extending this theory to describing HHG and above threshold ionization (ATI) processes. Furthermore, designing the “re-scattering electron trajectories” reconstruction scheme based on the electron trajectories with response time correction will provide important suggestions for HHG spectroscopic experiments. Finally, considering the asymmetric ionization caused by the PD effect of polar molecules, if the net ionization yield of adjacent sub-cycles is used as the current indicator, polar molecules can be used as a “micro diode” to study a type of attosecond response switching device. Polar molecular diodes emit electrons through tunneling ionization in laser field. According to the response time theory, tunneling occurs almost instantaneously, and response time needs considering only at the tunneling exit. Based on this, by searching for suitable materials (such as two-dimensional materials), it is possible to design a type of semi-classical diode (which can utilize tunneling) with femtosecond or even sub-femtosecond response time. The response time theory can provide a convenient theoretical tool for designing of such tunneling diodes.
To time-resolve attosecond electronic dynamics in general photoionization processes, the technique that retrieves the phase of emitted electronic wave packets without intercepting the interactions is essential. Here, we theoretically demonstrate a scheme that uses isolated attosecond pulses (IAPs) to achieve this goal. Our approach utilizes the coherent interference between the electronic wave packets of interest and the one produced by a subsequent IAP. It is shown that the photoelectron spectral phase that has eluded direct detection so far can be fully recovered from observable photoelectron spectra without perturbing the electron-release process under investigation. By further performing a time-frequency-like analysis on the photoelectron energy spectra with the spectral phase, we reveal the birth processes of photoelectrons in time and the association between electronic energy and birth time in strong-field ionization driven by circularly polarized laser pulses. The present work explores a promising application of IAPs for ultrafast measurement and opens a viable venue for investigating electronic dynamics with quantum phase information.
To measure and control the electron motion in atoms and molecules by the strong laser field on the attosecond time scale is one of the research frontiers of atomic and molecular photophysics. It involves many new phenomena and processes and raises a series of questions of concepts, theories, and methods. Recent studies show that the Coulomb potential can cause the ionization time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum. This lag can be understood as the response time of the electronic wave function to the strong-field-induced ionization event. It has a profound influence on the subsequent ultrafast dynamics of the ionized electron and can significantly change the time–frequency properties of electron trajectory (an important theoretical tool for attosecond measurement). Here, the research progress of response time and its implications on attosecond measurement are briefly introduced.