Probing laser-driven bound-state dynamics using attosecond streaking spectroscopy

Xi Chen, Wei Cao, Zhiting Li, Zhen Yang, Qingbin Zhang, and Peixiang Lu

Phys. Rev. A 102, 053119 – Published 30 November 2020

Abstract

When an atom or molecule is illuminated by a short laser pulse, the intense electric field couples different electronic states promptly and alters the final products. Detecting such interaction processes in a time-resolved way requires techniques with unprecedented time resolution and is important for applications such as coherent chemical reaction control. Here by solving the time-dependent Schrödinger equation, we demonstrate that the time evolution of complex amplitudes of bound electronic states during the interaction with an optical laser pulse can be extracted with high accuracy using attosecond streaking.

Received 7 August 2020
Revised 26 October 2020
Accepted 9 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.053119

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields Photoemission Ultrafast phenomena

Atoms

Rotating wave approximation Schroedinger equation Strong-field approximation Ultrafast pump-probe spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Xi Chen¹, Wei Cao ^1,*, Zhiting Li ¹, Zhen Yang¹, Qingbin Zhang¹, and Peixiang Lu^1,2,†

¹School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
²Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430205, China

^*weicao@hust.edu.cn
^†lupeixiang@mail.hust.edu.cn

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Issue

Vol. 102, Iss. 5 — November 2020

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Images

Figure 1
Reconstruction of a field-free bound wave packet. (a) Schematic view of the XUV ionization process. The energy spectrum of the model atom is presented, where $E_{1} = - 23.5 eV$ , $E_{3} = - 4.5 eV$ , $E_{4} = - 2.7 eV,$ and $E_{7} = - 0.98 eV$ . The XUV pulse spanning from 85 to $125 eV$ is chosen to ionize the electron from different bound states. (b) Simulated photoelectron spectrum from the model atom, prepared in an initial state $| ψ_{0} 〉 = 1 / \sqrt{2} | 3 〉 + 1 / \sqrt{2} | 4 〉$ , without the streaking field. The photoelectron yield is normalized. (c) The real and imaginary components of the retrieved phase gate $G (t)$ from (a) by using PCGP algorithm. (d) Fourier transform of $g (t)$ . The energy of each peak $| n 〉$ is corrected by subtracting $E_{m}$ from $- Δ E_{n m}$ , then the exact binding energy $- E_{n}$ is obtained. (e) The retrieved and simulated time-dependent population of $| 3 〉$ and $| 4 〉$ . Note that all the simulated and retrieved population are sitting on top of each other.
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Figure 2
Reconstruction of a laser-driven singlet state. (a) Simulated attosecond streaking spectrogram from an excited atom prepared in a singlet state $| 3 〉$ . The electric field is a $670 nm$ , four cycles optical pulse with a peak intensity of $4 \times 10^{11} {W/cm}^{2}$ combined with a $100 as$ , $105 eV$ XUV pulse. (b) A conventional reference spectrogram calculated from an atom in the ground state $| 1 〉$ with the same optical pulses, except the XUV central energy is $125 eV$ . (c) Fourier transform of the retrieved $g (t)$ . Contributions from the rotating wave and counter-rotating wave terms are labeled by ${| n 〉}_{RWT}$ and ${| n 〉}_{CRT}$ , respectively. (d) The extracted time-dependent population (dashed line) of $| 3 〉$ , $| 4 〉$ , $| 7 〉$ , and $| 9 〉$ states compare with TDSE simulation (solid line).
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Figure 3
Reconstruction of a laser-driven superposed state in a resonant condition. Same as Fig. 2, but for an atom initially prepared in a superposed state $| ψ_{0} 〉 = 1 / \sqrt{2} | 3 〉 + 1 / \sqrt{2} | 4 〉$ .
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Figure 4
Reconstruction of a laser-driven superposed state in a detuned condition. Same as Fig. 3, but for a detuned optical field ( $λ_{L} = 750 nm$ ).
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Figure 5
Phase characterization of the laser-driven superposed state in detuned condition. (a) The retrieved phase evolution of $| 3 〉$ (dash line) extracted from peak ${| 3 〉}_{R T W}$ in Fig. 4, and compared to the TDSE simulation (solid line). The center of both retrieved and simulated phase evolution is shifted to 0. The dotted line indicated the time-dependent population of $| 3 〉$ . (b) Same as (a), but for excited state $| 4 〉$ .
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