Electron-positron pair production in frequency modulated laser fields

C. Gong, Z. L. Li, B. S. Xie, and Y. J. Li

Phys. Rev. D 101, 016008 – Published 8 January 2020

Abstract

The momentum spectrum and the number density of created electron-positron pairs in a frequency modulated laser field are investigated using the quantum kinetic equation. It is found that the momentum spectrum presents an obvious interference pattern. This is an imprint of the frequency modulated field on the momentum spectrum, because the momentum peaks correspond to the pair production process by absorbing different frequency component photons. Moreover, the interference effect can also be understood qualitatively by analyzing turning-point structures. The study of the pair number density shows that the number density is very sensitive to modulation parameters and can be enhanced by 2 or 3 orders of magnitude for certain modulation parameters, which may provide a new way to increase the number of created electron-positron pairs in future experiments.

Received 25 July 2019
Revised 13 December 2019

DOI:https://doi.org/10.1103/PhysRevD.101.016008

Physics Subject Headings (PhySH)

Quantum electrodynamics Quantum kinetic theory

Statistical Physics & ThermodynamicsParticles & Fields

Authors & Affiliations

C. Gong ¹, Z. L. Li ^1,2,*, B. S. Xie^3,4,†, and Y. J. Li^1,‡

¹State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China
²School of Science, China University of Mining and Technology, Beijing 100083, China
³Key Laboratory of Beam Technology of the Ministry of Education, and College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
⁴Beijing Radiation Center, Beijing 100875, China

^*zlli@cumtb.edu.cn
^†bsxie@bnu.edu.cn
^‡lyj@aphy.iphy.ac.cn

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Issue

Vol. 101, Iss. 1 — 1 January 2020

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Images

Figure 1
The Fourier transform of the frequency modulated electric field Eq. (4) with modulation parameters (a) $ω_{m} = 0.07 m$ , $b = 1.0$ and (b) $ω_{m} = 0.01 m$ , $b = 9.52$ . Some typical values of frequency peaks are labeled on both panels. Other field parameters are $E_{0} = 0.1 E_{cr}$ , $ω = 0.5 m$ , and $τ = 100 / m$ .
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Figure 2
The Fourier transform of the frequency modulated electric field, where the values of modulation parameter $(ω_{m}, b)$ are (0.01, 1.52) for the upper panel and (0.009, 9.52) for the lower panel. And the values of dominant frequency peaks are shown. Other field parameters are $E_{0} = 0.1 E_{cr}$ , $τ = 100 / m$ , $ω = 0.5 m$ .
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Figure 3
Contour plots of $| Ω (p, t) |^{2}$ in the complex $t$ plane, showing the location of turning points where $Ω (p, t) = 0$ . For the upper three panels from left to right the modulation frequency and momentum correspond to $ω_{m} = 0$ , $p_{1} = 0.08 m$ ; $ω_{m} = 0.07 m$ , $p_{5} = 0.356 m$ ; $ω_{m} = 0.1 m$ , $p_{11} = 0.44 m$ , respectively, and $b = 1.0$ . For the lower three panels from left to right the momentum values are $p_{16}$ , $p_{17}$ , and $p_{18}$ , respectively. The modulation parameters are the same as in Figs. 2, 1, and 2, respectively. Other field parameters are $E_{0} = 0.1 E_{cr}$ , $ω = 0.5 m$ , and $τ = 100 / m$ .
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Figure 4
The momentum spectra of created pairs in the modulated electric field with different modulation parameters. The modulation frequencies for (a)–(c) are $ω_{m} = 0.00, 0.07 m$ and $0.10 m$ , respectively. The degree of modulation is $b = 1.0$ . The modulation parameters ( $ω_{m}$ , b) for (d)–(f) are (0.01, 1.52), (0.01, 9.52), and (0.009, 9.52), respectively. Other field parameters are $E_{0} = 0.1 E_{cr}$ , $ω = 0.5 m$ , and $τ = 100 / m$ .
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Figure 5
The number of the created $e^{-} e^{+}$ pairs under the modulated electric field. The red short dash, black dash dot, and blue dot line are the dividing line between the degree of frequency modulation. The white points $A$ , $C$ , $E$ , $G$ , $I$ , $K$ represent the zone-minimum values for each region, while the black points $B$ , $D$ , $F$ , $H$ , $J$ , $L$ represent the zone-maximum values. From left to right, the electric field strength $E_{0} = 0.1 E_{cr}$ , $0.01 E_{cr}$ , and $0.1 E_{cr}$ , respectively, and the laser frequency $ω = 0.5 m$ , $0.5 m$ , and $0.05 m$ , respectively. The other parameters $τ = 100 / m$ , $b$ and $ω_{m}$ are variables.
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Figure 6
The number density of created electron-positron pairs as a function of field frequency $ω$ . The oscillating structures are related to the $n$ -photon thresholds. The upper line corresponds to $E_{0} = 0.1 E_{cr}$ and the lower line corresponds to $E_{0} = 0.01 E_{cr}$ . Other field parameters are $τ = 100 / m$ . Note that there is no frequency modulation, i.e., $b = 0$ .
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