Imprints of multielectron polarization effects in odd-even harmonic generation from CO molecules

Hien T. Nguyen, Kim-Ngan H. Nguyen, Ngoc-Loan Phan, Cam-Tu Le, DinhDuy Vu, Lan-Phuong Tran, and Van-Hoang Le

Phys. Rev. A 105, 023106 – Published 11 February 2022

Abstract

Dynamic core-electron polarization (DCeP) is a correction to the single-active electron (SAE) approximation by considering a response of the core electrons to the time-dependent laser field. Despite being initially construed as a perturbative correction, in some cases especially atoms and molecules with large polarizabilities, DCeP can qualitatively alter predictions produced by the bare SAE theory. In this study, we unambiguously demonstrate the nonperturbative role of DCeP in the resolved odd-even high-order harmonic generation (HHG) of the CO molecule. In particular, we find that the even-to-odd ratio, i.e., the ratio between the harmonic intensities of even order and average of the two adjacent odd orders, changes by as much as one order of magnitude when DCeP is included, making the theoretically predicted values remarkably consistent with the experimental ones. This strong manifestation allows us to verify the DCeP role in HHG by experimental data. Furthermore, our analysis of the harmonic time profile shows that this agreement is not an artifact of the numerical method but reflects relevant physics, establishing that DCeP must be incorporated into the standard framework for strong-field physics.

Received 28 September 2021
Revised 21 December 2021
Accepted 21 January 2022

DOI:https://doi.org/10.1103/PhysRevA.105.023106

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields High-order harmonic generation

Atomic, Molecular & Optical

Authors & Affiliations

Hien T. Nguyen ^1,2,3, Kim-Ngan H. Nguyen ^4,5, Ngoc-Loan Phan ^6,7,*, Cam-Tu Le ^8,9,†, DinhDuy Vu ⁶, Lan-Phuong Tran ⁷, and Van-Hoang Le ^6,7,‡

¹Department of Theoretical Physics, University of Science, Ho Chi Minh City 72711, Vietnam
²Vietnam National University, Ho Chi Minh City 70000, Vietnam
³Department of Physics, Tay Nguyen University, Buon Ma Thuot City 63161, Vietnam
⁴Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City 71008, Vietnam
⁵Faculty of Natural Sciences, Duy Tan University, Da Nang City 50000, Vietnam
⁶Computational Physics Laboratory K002, Ho Chi Minh City University of Education, Ho Chi Minh City 72711, Vietnam
⁷Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City 72711, Vietnam
⁸Atomic Molecular and Optical Physics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City 72912, Vietnam
⁹Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 72912, Vietnam

^*Corresponding author: loanptn@hcmue.edu.vn
^†lethicamtu@tdtu.edu.vn
^‡hoanglv@hcmue.edu.vn

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Vol. 105, Iss. 2 — February 2022

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Images

Figure 1
The CO model and molecular frame. An electric field aligned along the unit vector $e$ makes with the molecular axis an orientation angle $θ$ .
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Figure 2
The simulated even-to-odd ratios of the CO molecules with DCeP ( $SAE + P$ ) (solid line) and without DCeP (SAE) (dashed line). The 800-nm laser pulse with the intensity of 1.5 $\times 10^{14} W / {cm}^{2}$ is used. The experimental data are taken from Refs. [24] (blue crosses) and [25] (green open hexagons) for the 800-nm laser pulse with intensities of 1.5 $\times 10^{14} W / {cm}^{2}$ and 2.2 $\times 10^{14} W / {cm}^{2}$ , respectively. The break interval in $y$ axis is $[2.5, 2.7]$ , dividing the figure into two spaces with different scales. The experimental even-to-odd ratios match the theoretical ones with the DCeP effect.
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Figure 3
The time profile intensity [(a), (c)] and phase [(b), (d)] for orders 16 and 22 from theoretical models without (SAE) and with DCeP ( $SAE + P$ ). The lasers with the same parameters as used in Fig. 2 but with the laser intensity of 1.5 $\times 10^{14} W / {cm}^{2}$ . The red and black circles indicate the peaks of attosecond bursts when ignoring and including DCeP, respectively.
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Figure 4
The illustration of $κ (n)$ (a) and $- cos Δ ϕ (n)$ (b) calculated from the two adjacent attosecond bursts emitted around $4.76 T_{0}$ and $5.25 T_{0}$ for the cases without (SAE) and with DCeP ( $SAE + P$ ). In panel (c), the even-to-odd ratio calculated by Eq. (6) is compared to the result from TDSE when considering DCeP. The laser parameters are the same as in Fig. 3. The phase difference between the adjacent attosecond bursts and the even-to-odd ratio have similar modulation with harmonic energy.
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Figure 5
The separated odd- and even-harmonic spectra [(a), (b)] and the even-to-odd ratios when considering both long and short [(c), (d)], or only short [(e), (f)] trajectories of ionized electrons. In panels (c)–(f), the horizontal dotted gray lines show the even-to-odd ratio equals one. The laser parameters are wavelength of 800 nm and various intensities [(c), (e)]; and intensity of 1.5 $\times 10^{14} W / {cm}^{2}$ and various wavelengths [(d), (f)]. The notation $I_{0}$ in the figures stands for 1.0 $\times 10^{14} W / {cm}^{2}$ . The molecular orientation angle is $0^{\circ}$ . The DCeP effect is included. The elimination of long trajectories smooths the odd- and even-harmonic spectra and the even-to-odd ratios. Moreover, the even-to-odd ratios are stable with changing laser intensities (e) and wavelengths (f).
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Figure 6
The simulated even-to-odd ratios for parallel (upper panels) and perpendicular (lower panels) HHG spectra from CO molecules without (SAE) and with the DCeP effect ( $SAE + P$ ) in the case of orientation angles of $30^{\circ}$ [(a), (b)] and $75^{\circ}$ [(c), (d)]. The 800-nm laser pulse with the intensity of 1.5 $\times 10^{14} W / {cm}^{2}$ is used. The DCeP affects both the magnitude and shape of the even-to-odd ratio of parallel and perpendicular HHGs.
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