Acta Photonica Sinica, Volume. 54, Issue 1, 0132001(2025)

Streaking Time Delay and the Oscillation Amplitude of the Momentum Shift

Mengfei XIE and Weichao JIANG*
Author Affiliations
  • Institute of Quantum Precision Measurement,College of Physics and Optoelectronic Engineering,Shenzhen University,Shenzhen 518060,China
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    In usual attosecond streaking schemes, an Extreme Ultraviolet (XUV) pulse of a few hundred attoseconds serving as a pump and a phase-controlled few-cycle Infrared (IR) pulse as a probe. XUV photon can excite the bound electron in atoms to continuum states, resulting in ionization. The ionized electrons can then be accelerated, decelerated, or deflected by the external IR laser field, generating attosecond-level temporal resolution. In the presence of a polarized IR laser pulse, ionization of a bound electron is achieved by absorbing an XUV photon, the energy of the photoelectron ejected forward along the laser polarization is affected by the attosecond streaking of the external IR pulse and depends on the phase of the IR pulse at the moment of ionization. By analyzing attosecond streaking spectra, the photoemission delay can be determined from the final kinetic energy oscillation associated with the relative delay between XUV and IR fields. Both the streaking time delay and amplitude of the energy oscillation depend on the coupling of the potential and the detected IR field. The determination of streaking time delay is a complex task that involves taking into account a variety of effects, such as the Eisenbud-Wigner-Smith (EWS) time delay,Coulomb-Laser Coupling (CLC), electron correlation and dipole-laser coupling. In the context of streaking time delay for ground-state hydrogenic atoms, it is commonly acknowledged that two factors account for this delay. The first is the EWS delay, resulting from the potential's short-range behavior. The second is the CLC delay, due to the joint influence of the IR pulse and the long-range Coulomb potential. Attosecond streaking provides unprecedented insights into the dynamics of time-resolved photoelectron emission in atoms. Moreover, in addition to conventional linearly polarized fields, researchers have recently combined bicircular fields with streaking. This approach enables ionization-time retrieval with remarkable few-attosecond precision. While exploring the streaking dynamics, most of the aforementioned reports have focused mainly on the streaking time delay and have not discussed the oscillation amplitude of the momentum shift of the electron, which defines the strength of the IR field if measured from the spectra, explicitly. However, to truly understand the dynamics, we need to consider the oscillation amplitudeκin addition to the streaking time delay. For low kinetic energies of photoelectrons, κ is greater than 1, while for high kinetic energies, κ approaches the SFA limit of 1. The duration of XUV pulses also has a significant impact on the amplitude of momentum displacement oscillations.In this work, by solving the three-dimensional time-dependent Schr?dinger equations for helium atoms and establishing a numerical analytical model for Weak Field Approximation (WFA), the streaking time delay and oscillation amplitude of the momentum shift were studied. Our findings show that altering the energy of XUV photons and the wavelength of infrared light has a significant impact on both the streaking time delay and the amplitude of momentum shift. Additionally, although the streaking time delay is not sensitive to changes in the duration of the XUV pulse, the oscillation amplitude does changes. The WFA model effectively explains this phenomenon observed in TDSE calculations by accounting for the fact that photoelectrons can be ionized not only at the peak of the XUV pulse but also during times when the XUV field is not negligible. Through averaging over the initial ionization times, we have obtained an analytical estimation for the XUV duration dependence of the κ oscillation amplitude. This equation accurately describes the reduction in the κ amplitude observed in TDSE calculations with increasing XUV pulse duration. The Coulomb effect has a significant impact on the streaking method. Therefore, we used two different model potentials to calculate helium atoms and investigated the influence of different initial electron emission positions on the streaking time delay and oscillation amplitude of the momentum shift. It was found that both the streaking time delay and the oscillation amplitude of the momentum shift are greatly influenced by the choice of initial ionization position. Ultimately, it was discovered that only when the initial ionization position for helium atoms is selected near 0.87 a.u., can we achieve a good agreement between TDSE results and the WFA results. The WFA model, by simplifying the electron's trajectory into a classical mechanics problem, transforms the abstract quantum dynamical process into a series of intuitively understandable electron motions and energy changes, providing an intuitive framework to comprehend the electron's behavior in both XUV and IR fields.

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    Mengfei XIE, Weichao JIANG. Streaking Time Delay and the Oscillation Amplitude of the Momentum Shift[J]. Acta Photonica Sinica, 2025, 54(1): 0132001

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    Paper Information

    Category: Ultrafast Optics

    Received: Jun. 28, 2024

    Accepted: Aug. 19, 2024

    Published Online: Mar. 5, 2025

    The Author Email: JIANG Weichao (jiang.wei.chao@szu.edu.cn)

    DOI:10.3788/gzxb20255401.0132001

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