Sauter-Schwinger pair creation dynamically assisted by a plane wave

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Sauter-Schwinger pair creation dynamically assisted by a plane wave

Greger Torgrimsson, Christian Schneider, and Ralf Schützhold

Phys. Rev. D 97, 096004 – Published 7 May 2018

Abstract

We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Received 11 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.096004

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonperturbative effects in field theory Particle production Quantum electrodynamics Schwinger effect

Particles & Fields

Authors & Affiliations

Greger Torgrimsson^1,2,3, Christian Schneider¹, and Ralf Schützhold¹

¹Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
²Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
³Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany

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Issue

Vol. 97, Iss. 9 — 1 May 2018

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Images

Figure 1
Plot of the exponent of the pair-creation probability $P_{e^{+} e^{-}}$ as a function of $γ$ for perpendicular incidence and parallel polarization (2) with $ϵ = 10^{- 2}$ (top) and $ϵ = 10^{- 3}$ (bottom). The exponent has been multiplied by $q E / m^{2}$ , i.e., the plot shows $f (γ)$ such that $P_{e^{+} e^{-}} \sim \exp {- f (γ) m^{2} / [q E]}$ . The circles represent the numerical world-line instanton results from Sec. 4, and the dashed curve corresponds to the large- $γ$ approximation in (9). The solid curve shows the result of our improved analytical approximation obtained by inserting the dominant order $N_{*}$ from Eq. (11) into Eq. (4). The constant factor in Eq. (11) has been chosen in order to match the world-line instanton results, which gives a factor of 8 for $ϵ = 10^{- 2}$ (top) and a factor of 9.5 for $ϵ = 10^{- 3}$ (bottom). With these values, we observe good agreement between our improved analytical approximation and the numerical world-line instanton results.
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Figure 2
Same as Fig. 1, but for perpendicular polarization $e_{P}^{⊥}$ as discussed in Sec. 3. Again, the constant factor in Eq. (11) is obtained by fitting and gives 1.9 for $ϵ = 10^{- 2}$ (top) and 2 for $ϵ = 10^{- 3}$ (bottom). We observe that perpendicular polarization yields a lower pair-creation probability $P_{e^{+} e^{-}}$ .
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Figure 3
Worldline instantons (in units of $m / q E$ ) for the case of parallel polarization with $ϵ = 10^{- 2}$ and $γ = m Ω / q E$ ranging from 0 to 15. The purple circle in the $x_{1} = 0$ -plane is the circular instanton in the limit $γ \to 0$ . For increasing values of $γ$ the instantons shrink (predominantly in the $x_{3}$ -direction) and rotate in the $ℑ (x_{1}) - x_{4}$ -plane.
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Figure 4
Pair production probabilities for different values of the combined Keldysh parameter $γ$ , strong field strength $E = E_{S} / 30$ (corresponding to a laser intensity of $I \approx 5 \times 10^{26} W / {cm}^{2}$ ) and weak field $ϵ = 10^{- 2}$ . We have assumed a spacetime volume of $1 μ m^{4}$ . As shown before, the case of parallel polarization yields stronger enhancement. Further, the spin factor does not contribute in the parallel case, while it enhances pair production in the perpendicular case. The values $Ω = 500 keV$ or $Ω = 1 MeV$ considered in [25], for example, would correspond to $γ = 30$ or $γ = 60$ , respectively, and hence result in a drastic enhancement. Unfortunately, however, these values are probably outside the range of near future XFELs. Lower values such as 25 keV [39] correspond to $γ = 3 / 2$ (when $E = E_{S} / 30$ ) and are thus not sufficient for an exponential enhancement. On the other hand, for lower field strengths such as $E = E_{S} / 100$ , the same frequency of 25 keV would correspond to $γ = 5$ where we start to see exponential enhancement. However, the total probabilities for $E = E_{S} / 100$ are much lower and thus very hard to detect.
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Figure 5
These plots show our three estimates of the dominant order for perpendicular polarization. The dashed lines are obtained from Eq. (11), the solid lines show (b2), and the circles show (b4), in which $P_{e^{+} e^{-}}$ is the total probability for spinor QED, including the prefactor. The third approach gives negative $N_{*}$ below the threshold, but that is just another sign (c.f. Fig. 4) that the instanton prediction of the prefactor breaks down in that regime [42].
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