Quantum Interference of Glory Rescattering in Strong-Field Atomic Ionization

Q. Z. Xia, J. F. Tao, J. Cai, L. B. Fu, and J. Liu

Phys. Rev. Lett. 121, 143201 – Published 3 October 2018

Abstract

During the ionization of atoms irradiated by linearly polarized intense laser fields, we find for the first time that the transverse momentum distribution of photoelectrons can be well fitted by a squared zeroth-order Bessel function because of the quantum interference effect of glory rescattering. The characteristic of the Bessel function is determined by the common angular momentum of a number of semiclassical paths termed as glory trajectories, which are launched with different nonzero initial transverse momenta distributed on a specific circle in the momentum plane and finally deflected to the same asymptotic momentum, which is along the polarization direction, through post-tunneling rescattering. Glory rescattering theory based on the semiclassical path-integral formalism is developed to address this effect quantitatively. Our theory can resolve the long-standing discrepancies between existing theories and experiments on the fringe location, predict the sudden transition of the fringe structure in holographic patterns, and shed light on the quantum interference aspects of low-energy structures in strong-field atomic ionization.

Received 4 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.143201

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields

Atomic, Molecular & Optical

Authors & Affiliations

Q. Z. Xia¹, J. F. Tao^1,2, J. Cai³, L. B. Fu^4,5, and J. Liu^1,5,*

¹National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
²Beijing Computational Science Research Center, Beijing 100193, China
³School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
⁴Graduate School of China Academy of Engineering Physics, Beijing 100193, China
⁵CAPT, HEDPS, and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing 100871, China

^*liu_jie@iapcm.ac.cn

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Issue

Vol. 121, Iss. 14 — 5 October 2018

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Images

Figure 1
(a) Glory scattering during the forward rescattering after electron tunneling. Traditional two-path (magenta) interference and glory interference of an infinite number of paths (green trajectory and its rotational counterparts) that approach the same final momentum. For details, refer to the text. (b) Axial caustic singularity in glory scattering: GTs projected on the transverse momentum plane, which are launched from the red circle and finally converge at the origin. (c) Illustration of glory scattering of localized wave packet. Transverse momentum distribution after scattering in laser-field-free model of 2D (d) and 1D (e). The incident wave packet is $ψ_{0} = \exp (- | \vec{r} - {\vec{r}}_{0} |^{2} + i {\vec{p}}_{0} \cdot \vec{r})$ , where ${\vec{r}}_{0} = (0, 0, - 40)$ and ${\vec{p}}_{0} = (0, 0, 0.5)$ . The 2D slice is obtained at $p_{z} = 0.5$ , while the 1D (black dot) is obtained at $p_{z} = 0.5$ and $p_{y} = 0$ . The curve of $J_{0}^{2} (b_{g} p_{x})$ is plotted with a red solid line in (e) for comparison.
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Figure 2
(a) Glory trajectories corresponding to $p_{z} = 0.2$ , 0.4, and 0.8 from top to bottom. (b) Transverse momentum distribution corresponding to $p_{z} = 0.2$ , 0.4, and 0.8. The squared Bessel function is plotted for comparison. (c) Simulated result (black squares) of the longitudinal momentum distribution and the prediction of GRT (red curve). (d) Simulated (black squares) longitudinal distribution that removes inter- and intracycle interference, the prediction of GRT (red curve), and that of the classical trajectory Monte Carlo (CTMC) method (blue dashed line). The simulated momentum spectrum is obtained by solving the TDSE of the hydrogen atom. The laser wavelength is 800 nm and the intensity is $87 TW / {cm}^{2}$ . The black line in panel (c) denotes the position corresponding to 2 times ponderomotive potential ( $2 U_{p}$ ).
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Figure 3
Experimental holographic pattern and positions of the first dark fringe calculated by SFA (orange open circles), CCSFA (purple solid triangles), and GRT [red solid line in (a) and green in (b)]. The experimental data of the metastable ( $6 s$ ) Xe atoms in (a) are extracted from Ref. [15] as well as SFA and CCSFA results, and that in (b) using argon is extracted from Ref. [16]. The laser parameters are (a) wavelength of 7000 nm and intensity of $7.1 \times 10^{11} W / {cm}^{2}$ , and (b) wavelength of 1300 nm and intensity of $7.5 \times 10^{13} W / {cm}^{2}$ .
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Figure 4
$l_{g}$ of the GT with respect to their asymptotic momentum $p_{z}$ , or electron energy $E_{k} = p_{z}^{2} / 2$ , is represented by the black solid line. The angle-resolved photoelectron energy spectrum along the polarization direction, i.e., $P (E_{k}, θ = 0) \sim ϖ P_{⊥ g} l_{g}$ , is plotted with a blue dashed line. For comparison, the result of $ϖ P_{⊥ g}$ is plotted with the magenta short dashed line. Ar atoms are used. The laser parameters are the same as in Fig. 3.
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