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Matter and Radiation at Extremes
Vol. 7, Issue 1, 014401 (2022)

Photon polarization effects in polarized electron–positron pair production in a strong laser field

Ya-Nan Dai¹, Bai-Fei Shen^1、2, Jian-Xing Li³, Rashid Shaisultanov^4、5, Karen Z. Hatsagortsyan⁴, Christoph H. Keitel⁴, and Yue-Yue Chen^1、a)

Author Affiliations

¹Department of Physics, Shanghai Normal University, Shanghai 200234, China

²State Key Laboratory of High Field Laser Physics and CAS Center for Excellence in Ultra-intense Laser Science, Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences (CAS), Shanghai 201800, China

³School of Physics, Xi’an Jiaotong University, Xi’an 710049, China

⁴Max-Planck-Institut fur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

⁵Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany

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DOI: 10.1063/5.0063633 Cite this Article

Ya-Nan Dai, Bai-Fei Shen, Jian-Xing Li, Rashid Shaisultanov, Karen Z. Hatsagortsyan, Christoph H. Keitel, Yue-Yue Chen. Photon polarization effects in polarized electron–positron pair production in a strong laser field[J]. Matter and Radiation at Extremes, 2022, 7(1): 014401 Copy Citation Text

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Abstract

Deep understanding of the impact of photon polarization on pair production is essential for the efficient generation of laser-driven polarized positron beams and demands a complete description of polarization effects in strong-field QED processes. Employing fully polarization-resolved Monte Carlo simulations, we investigate correlated photon and electron (positron) polarization effects in the multiphoton Breit–Wheeler pair production process during the interaction of an ultrarelativistic electron beam with a counterpropagating elliptically polarized laser pulse. We show that the polarization of e^-e⁺ pairs is degraded by 35% when the polarization of the intermediate photon is resolved, accompanied by an ∼13% decrease in the pair yield. Moreover, in this case, the polarization direction of energetic positrons at small deflection angles can even be reversed when high-energy photons with polarization parallel to the laser electric field are involved.

{\vec{e}}_{1} = \vec{s} - \vec{n} (\vec{n} \cdot \vec{s}), {\vec{e}}_{2} = \vec{n} \times {\vec{e}}_{1} .

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\begin{align} d W_{r} = \frac{1}{2} (d W_{11} + d W_{22}) + \frac{1}{2} ξ_{1} (d W_{11} - d W_{22}) \\ - i \frac{1}{2} ξ_{2} (d W_{21} - d W_{12}) + \frac{1}{2} ξ_{3} (d W_{11} - d W_{22}) \\ = \frac{1}{2} (F_{0} + ξ_{1} F_{1} + ξ_{2} F_{2} + ξ_{3} F_{3}), \end{align}

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\begin{align} F_{0} = \frac{α}{2 \sqrt{3} π γ^{2}} d ω \{[\frac{ε^{2} + ε^{' 2}}{{ε ε}^{'}} K_{2 / 3} (z_{q}) - \int_{z_{q}}^{\infty} d x K_{1 / 3} (x)] \\ + [2 K_{2 / 3} (z_{q}) - \int_{z_{q}}^{\infty} d x K_{1 / 3} (x)] ({\vec{ζ}}_{i} \cdot {\vec{ζ}}_{f}) \\ - K_{1 / 3} (z_{q}) [\frac{ω}{ε} ({\vec{ζ}}_{i} \cdot \vec{b}) + \frac{ω}{ε^{'}} ({\vec{ζ}}_{f} \cdot \vec{b})] \\ + \frac{ω^{2}}{ε^{'} ε} [K_{2 / 3} (z_{q}) - \int_{z_{q}}^{\infty} d x K_{1 / 3} (x)] ({\vec{ζ}}_{i} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{f} \cdot \vec{\hat{v}})\}, \end{align}

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\begin{align} F_{1} = & \frac{α}{2 \sqrt{3} π γ^{2}} d ω \{\frac{ε^{2} - ε^{' 2}}{2 ε^{'} ε} K_{2 / 3} (z_{q}) [\vec{\hat{v}} \cdot ({\vec{ζ}}_{f} \times {\vec{ζ}}_{i})] \\ + [\frac{ω}{ε^{'}} ({\vec{ζ}}_{i} \cdot \vec{s}) + \frac{ω}{ε} ({\vec{ζ}}_{f} \cdot \vec{s})] K_{1 / 3} (z_{q}) \\ - \frac{ω^{2}}{2 ε^{'} ε} \int_{z_{q}}^{\infty} d x K_{1 / 3} (x) [({\vec{ζ}}_{i} \cdot \vec{s}) ({\vec{ζ}}_{f} \cdot \vec{b}) + ({\vec{ζ}}_{i} \cdot \vec{b}) ({\vec{ζ}}_{f} \cdot \vec{s})]\}, \end{align}

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\begin{align} F_{2} = & - \frac{α}{2 \sqrt{3} π γ^{2}} d ω \{\frac{ε^{2} - ε^{' 2}}{2 ε^{'} ε} K_{1 / 3} (z_{q}) [\vec{s} \cdot ({\vec{ζ}}_{f} \times {\vec{ζ}}_{i})] \\ + [- \frac{ε^{2} - ε^{' 2}}{ε^{'} ε} K_{2 / 3} (z_{q}) + \frac{ω}{ε} \int_{z_{q}}^{\infty} d x K_{1 / 3} (x)] ({\vec{ζ}}_{i} \cdot \vec{\hat{v}}) \\ + [- \frac{ε^{2} - ε^{' 2}}{ε^{'} ε} K_{2 / 3} (z_{q}) + \frac{ω}{ε^{'}} \int_{z_{q}}^{\infty} d x K_{1 / 3} (x)] ({\vec{ζ}}_{f} \cdot \vec{\hat{v}}) \\ + \frac{ω^{2}}{2 ε^{'} ε} K_{1 / 3} (z_{q}) [({\vec{ζ}}_{i} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{f} \cdot \vec{b}) + ({\vec{ζ}}_{i} \cdot \vec{b}) ({\vec{ζ}}_{f} \cdot \vec{\hat{v}})]\}, \end{align}

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\begin{align} F_{3} = & \frac{α}{2 \sqrt{3} π γ^{2}} d ω \{K_{2 / 3} (z_{q}) + \frac{ε^{2} + ε^{' 2}}{2 ε^{'} ε} K_{2 / 3} (z_{q}) ({\vec{ζ}}_{i} \cdot {\vec{ζ}}_{f}) \\ - [\frac{ω}{ε^{'}} ({\vec{ζ}}_{i} \cdot \vec{b}) + \frac{ω}{ε} ({\vec{ζ}}_{f} \cdot \vec{b})] K_{1 / 3} (z_{q}) \\ + \frac{ω^{2}}{2 ε^{'} ε} [- K_{2 / 3} (z_{q}) ({\vec{ζ}}_{i} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{f} \cdot \vec{\hat{v}}) + \int_{z_{q}}^{\infty} d x K_{1 / 3} (x) \\ \times [({\vec{ζ}}_{i} \cdot \vec{b}) ({\vec{ζ}}_{f} \cdot \vec{b}) - ({\vec{ζ}}_{i} \cdot \vec{s}) ({\vec{ζ}}_{f} \cdot \vec{s})]]\} . \end{align}

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\begin{align} \vec{e} = a_{1} {\vec{e}}_{1} + a_{2} {\vec{e}}_{2}, \end{align}

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\begin{align} {\vec{e}}_{1} & = \frac{\vec{E} - \vec{n} (\vec{n} \cdot \vec{E}) + \vec{n} \times \vec{B}}{| \vec{E} - \vec{n} (\vec{n} \cdot \vec{E}) + \vec{n} \times \vec{B} |}, \end{align}

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\begin{align} {\vec{e}}_{2} & = \vec{n} \times {\vec{e}}_{1}, \vec{n} = \frac{\vec{k}}{| \vec{k} |} . \end{align}

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\begin{align} d W_{p} & = \frac{1}{2} (d W^{(11)} + d W^{(22)}) + \frac{1}{2} ξ_{1} (d W^{(11)} - d W^{(22)}) \\ - i \frac{1}{2} ξ_{2} (d W^{(21)} - d W^{(12)}) + \frac{1}{2} ξ_{3} (d W^{(11)} - d W^{(22)}) \\ = \frac{1}{2} (G_{0} + ξ_{1} G_{1} + ξ_{2} G_{2} + ξ_{3} G_{3}), \end{align}

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\begin{align} G_{0} = \frac{α m^{2} d ε}{2 \sqrt{3} π ω^{2}} \{[\int_{z_{p}}^{\infty} d x K_{1 / 3} (x) + \frac{ε_{+}^{2} + ε^{2}}{ε_{+} ε} K_{2 / 3} (z_{p})] \\ + [\int_{z_{p}}^{\infty} d x K_{1 / 3} (x) - 2 K_{2 / 3} (z_{p})] ({\vec{ζ}}_{-} \cdot {\vec{ζ}}_{+}) \\ \!\!\!+ [\frac{ω}{ε_{+}} ({\vec{ζ}}_{+} \cdot \vec{b}) - \frac{ω}{ε} ({\vec{ζ}}_{-} \cdot \vec{b})] K_{1 / 3} (z_{p}) \\ + [\frac{ε_{+}^{2} + ε^{2}}{{ε ε}_{+}} \int_{z_{p}}^{\infty} d x K_{1 / 3} (x) \\ - \frac{{(ε_{+} - ε)}^{2}}{{ε ε}_{+}} K_{2 / 3} (z_{p})] ({\vec{ζ}}_{-} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{+} \cdot \vec{\hat{v}})\}, \end{align}

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\begin{align} G_{1} = & \frac{α m^{2} d ε}{2 \sqrt{3} π ω^{2}} \{- \frac{ε_{+}^{2} - ε^{2}}{2 ε_{+} ε} K_{2 / 3} (z_{p}) [\vec{\hat{v}} \cdot ({\vec{ζ}}_{+} \times {\vec{ζ}}_{-})] \\ + [\frac{ω}{ε} ({\vec{ζ}}_{+} \cdot \vec{s}) - \frac{ω}{ε_{+}} ({\vec{ζ}}_{-} \cdot \vec{s})] K_{1 / 3} (z_{p}) \\ - \frac{ω^{2}}{2 ε_{+} ε} \int_{z_{p}}^{\infty} d x K_{1 / 3} (x) [({\vec{ζ}}_{-} \cdot \vec{b}) ({\vec{ζ}}_{+} \cdot \vec{s}) + ({\vec{ζ}}_{-} \cdot \vec{s}) ({\vec{ζ}}_{+} \cdot \vec{b})]\}, \end{align}

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\begin{align} G_{2} =\!\!\!\! & \frac{α m^{2} d ε}{2 \sqrt{3} π ω^{2}} \{- \frac{ω^{2}}{2 ε_{+} ε} K_{1 / 3} (z_{p}) [\vec{s} \cdot ({\vec{ζ}}_{-} \times {\vec{ζ}}_{+})] \\ + [\frac{ω}{ε_{+}} \int_{z_{p}}^{\infty} d x K_{1 / 3} (x) + \frac{ε_{+}^{2} - ε^{2}}{ε_{+} ε} K_{2 / 3} (z_{p})] ({\vec{ζ}}_{+} \cdot \vec{\hat{v}}) \\ + [\frac{ω}{ε} \int_{z_{p}}^{\infty} d x K_{1 / 3} (x) - \frac{ε_{+}^{2} - ε^{2}}{ε_{+} ε} K_{2 / 3} (z_{p})] ({\vec{ζ}}_{-} \cdot \vec{\hat{v}}) \\ - \frac{ε_{+}^{2} - ε^{2}}{2 ε_{+} ε} K_{1 / 3} (z_{p}) [({\vec{ζ}}_{-} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{+} \cdot \vec{b}) + ({\vec{ζ}}_{-} \cdot \vec{b}) ({\vec{ζ}}_{+} \cdot \vec{\hat{v}})]\}, \end{align}

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\begin{align} G_{3} =\!\!\! & \frac{α m^{2} d ε}{2 \sqrt{3} π ω^{2}} \{- K_{2 / 3} (z_{p}) + \frac{ε_{+}^{2} + ε^{2}}{2 ε_{+} ε} K_{2 / 3} (z_{p}) ({\vec{ζ}}_{-} \cdot {\vec{ζ}}_{+}) \\ + [- \frac{ω}{ε} ({\vec{ζ}}_{+} \vec{b}) + \frac{ω}{ε_{+}} ({\vec{ζ}}_{-} \vec{b})] K_{1 / 3} (z_{p}) \\ - \frac{{(ε_{+} - ε)}^{2}}{2 ε_{+} ε} K_{2 / 3} (z_{p}) ({\vec{ζ}}_{-} \cdot \vec{\hat{v}}) ({\vec{ζ}}_{+} \cdot \vec{\hat{v}}) \\ + \frac{ω^{2}}{2 ε_{+} ε} \int_{z_{p}}^{\infty} d x K_{1 / 3} (x) [({\vec{ζ}}_{-} \cdot \vec{b}) ({\vec{ζ}}_{+} \cdot \vec{b}) - ({\vec{ζ}}_{-} \cdot \vec{s}) ({\vec{ζ}}_{+} \cdot \vec{s})]\} . \end{align}

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{\vec{ζ}}_{+}^{f, ξ} = \frac{ξ_{1} f_{3} \frac{ω}{ε} \vec{s} + ξ_{2} \vec{\hat{v}} (\frac{ω}{ε_{+}} f_{1} + \frac{ε_{+}^{2} - ε^{2}}{{ε ε}_{+}} f_{2}) + (\frac{ω}{ε_{+}} - ξ_{3} \frac{ω}{ε}) \vec{b} f_{3}}{f_{1} + \frac{ε^{2} + ε_{+}^{2}}{{ε ε}_{+}} f_{2} - ξ_{3} f_{2}} .

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{\vec{ζ}}_{+}^{f, 0} = \frac{\frac{ω}{ε_{+}} \vec{b} f_{3}}{f_{1} + \frac{ε^{2} + ε_{+}^{2}}{{ε ε}_{+}} f_{2}},

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{\vec{ζ}}^{f} = \frac{(2 f_{2} - f_{1}) {\vec{ζ}}_{i} - \frac{ω}{ε^{'}} \vec{b} f_{3} + \frac{ω}{ε^{'} ε} (f_{2} - f_{1}) ({\vec{ζ}}_{i} \cdot \vec{\hat{v}}) \vec{\hat{v}}}{\frac{ε^{2} + ε^{' 2}}{ε^{'} ε} f_{2} - f_{1} - \frac{ω}{ε} {\vec{ζ}}_{i} \cdot \vec{b} f_{3}},

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ξ_{3} = \frac{f_{2} - \frac{ω}{ε^{'}} ({\vec{ζ}}_{i} \cdot \vec{b}) f_{3}}{- f_{1} + \frac{ε^{2} + ε^{' 2}}{{ε ε}^{'}} f_{2} - \frac{ω}{ε} ({\vec{ζ}}_{i} \cdot \vec{b}) f_{3}},

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- f_{1} + \frac{ε^{2} + ε^{' 2}}{{ε ε}^{'}} f_{2} ≪ \frac{ω}{ε} f_{3}

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{\bar{ξ}}_{3} ({\vec{ζ}}_{i}) \approx {\bar{ξ}}_{3} (0) = f_{2} / (- f_{1} + \frac{ε^{2} + ε^{' 2}}{{ε ε}^{'}} f_{2}) \approx 0.51,

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{\bar{ζ}}_{y} (t) \propto {\bar{ζ}}_{y} (t_{i}) e^{- Ψ_{1} (χ_{e}) t},

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Ψ_{1} (χ_{e}) = \int_{0}^{\infty} \frac{u^{2} d u}{{(1 + u)}^{3}} K_{2 / 3} (\frac{2}{3} \frac{u}{χ_{e}}),

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Ya-Nan Dai, Bai-Fei Shen, Jian-Xing Li, Rashid Shaisultanov, Karen Z. Hatsagortsyan, Christoph H. Keitel, Yue-Yue Chen. Photon polarization effects in polarized electron–positron pair production in a strong laser field[J]. Matter and Radiation at Extremes, 2022, 7(1): 014401

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