Strong-Field Ionization of Hydrogen Atoms with Quantum Light

Yiqi Fang, Feng-Xiao Sun, Qiongyi He, and Yunquan Liu

Phys. Rev. Lett. 130, 253201 – Published 22 June 2023

Abstract

We study the strong-field ionization driven by quantum lights. Developing a quantum-optical-corrected strong-field approximation model, we simulate the photoelectron momentum distribution with squeezed-state light, which manifests as notably different interference structures from that with coherent-state (classical) light. With the saddle-point method, we analyze the electron dynamics and reveal that the photon statistics of squeezed-state light fields endows the tunneling electron wave packets with a time-varying phase uncertainty and modulates the photoelectron intracycle and intercycle interferences. Moreover, it is found the fluctuation of quantum light imprints significant influence on the propagation of tunneling electron wave packets, in which the ionization probability of electrons is considerably modified in time domain.

Received 21 November 2022
Accepted 31 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.253201

Physics Subject Headings (PhySH)

Quantum optics Strong field ionization & excitation

Atoms

Quantum correlations, foundations & formalism Strong-field approximation

Atomic, Molecular & Optical

Authors & Affiliations

Yiqi Fang ^1,*, Feng-Xiao Sun ^1,2,*, Qiongyi He ^1,2,3,4,†, and Yunquan Liu ^1,2,3,5,‡

¹State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
³Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, Jiangsu, China
⁴Hefei National Laboratory, Hefei 230088, China
⁵Beijing Academy of Quantum Information Sciences, Beijing 100193, China

^*These authors contributed equally to this work.
^†Corresponding author. qiongyihe@pku.edu.cn
^‡Corresponding author. Yunquan.liu@pku.edu.cn

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Issue

Vol. 130, Iss. 25 — 23 June 2023

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Images

Figure 1
(a) Illustration for the coherent state $| α_{0} ⟩$ of femtosecond quantum light at 800 nm. Left: generalized $P$ representation; upper right: electric field profile; bottom right: vector potential profile. (b) Photoelectron momentum distribution simulated with the quantum-optical-corrected strong-field approximation (QOSFA). (c),(d) Same as panels (a) and (b), in which a squeezed state light $| α_{0}, r ⟩$ is used. The squeezed parameter $r$ is given by $\sinh^{2} (r) = 0.0 05 | α_{0} |^{2}$ . The photoelectron wave packets ionized at different electric field peaks were labeled as $W_{1}$ , $W_{2}$ , $W_{3}$ , and $W_{4}$ , respectively. Here, $T_{800}$ is one cycle of 800-nm driving field. The electron intercycle interference, which forms annual rings as illustrated by the black dashed circle in (b), is largely suppressed in (d). In (c), $Δ α_{i}$ is used to quantify the phase fluctuation of electron wave packets as shown later.
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Figure 2
(a)–(d) Subcycle interferograms between different electron wave packets emitted in squeezed-state light. For comparison, the inset exhibits the same interferograms in coherent-state light. The electron wave packets involved in the interference have been indicated at the upper left corner. (e),(f) Normalized distributions of photoelectron yield along the dashed in (a)–(d). Interferences in (a) and (b) are the intracycle channels, and that in (c) and (d) are the intercycle channels. They are usually distinguished by the temporal interval of the ionization time of electron wave packets.
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Figure 3
Phase fluctuation of electron wave packets in the processes of (a) tunneling and (b) propagation. Different wave packets are distinguished by colors as shown in the inset of (a). The shaded regions indicate the phase uncertainties of electrons in squeezed light, and the solid lines represent the phase that is obtained with coherent light. (c) Ionization probability of electrons during propagation in squeezed light [Eq. (7)]. The black and red dashed lines indicate the turn-off moment of laser pulses and the ionization time of electrons, respectively. (d) Ionization probabilities of coherent and squeezed light at the ionization time. (e) The same as (d) but for the moment after the turn-off of laser pulses. For ease of comparison, the distributions in (c)–(e) have been normalized.
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Figure 4
Correlation between normalized ionization probability of electron wave packets and the electron phase uncertainty. As the phase uncertainty increases in the squeezed state light field, the ionization probability of photoelectrons drops off synchronously.
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