Carrier envelope phase and pulse shape effects on vacuum pair production in asymmetric electric fields with bell-shaped envelopes

TL;DR

The paper addresses how carrier-envelope phase (CEP) and pulse shape affect vacuum electron-positron pair production in time-dependent, asymmetric electric fields. It uses the quantum Vlasov equation (QVE) to compute momentum distributions and total densities for three bell-shaped envelopes (Gaussian, Lorentzian, Sauter) and applies a semiclassical turning-point analysis, regularized to handle non-analytic field profiles. Key findings show extreme sensitivity of both momentum spectra and yields to CEP, pulse asymmetry, and steepness, with multiphoton channels dominating in certain regimes and interference explained by turning-point structure; the number density can be enhanced by two to three orders of magnitude with suitable field parameters. The results highlight that careful optimization of pulse duration, envelope, and CEP can substantially maximize pair production, informing future high-intensity laser experiments and advancing understanding of nonperturbative QED vacuum decay.

Abstract

We investigate the combined effects of carrier envelope phase and laser pulse shape on electron-positron pair production in the presence of an external time-dependent asymmetric electric field by solving the quantum Vlasov equation. We analyze how the pulse asymmetry, the envelope type (Gaussian, Lorentzian and Sauter), and the carrier envelope phase jointly influence the momentum distribution and the number density of created pairs. Our results show that pair production exhibits extreme sensitivity to both the degree of temporal asymmetry and the steepness of the envelope on either side of the pulse. These effects are qualitatively explained through a turning-point analysis, which, for the first time, is carried out for a non-analytic electric field using a regularization scheme. We observed that multiphoton pair production dominates the Schwinger mechanism in the case of a long falling-pulse asymmetry. For a short falling pulse with a flat-topped profile, pair production is further facilitated. We demonstrate that the number density can be enhanced by two to three orders of magnitude by choosing certain field parameters.

Figures (13)

• Figure 1: Electric field with a Gaussian envelope for several combinations of $\beta$, $\varphi$ and $\nu$.
• Figure 2: Comparison of electric field profiles with Gaussian (dashed blue) and Sauter (solid red) envelopes with a large asymmetry parameter ($\beta =10$). Unlike the Gaussian case, the Sauter envelope does not become flatter as $\nu$ is increased.
• Figure 3: Momentum distribution $f_\textbf{k}(\infty)$ with $k_y = 0$ for a Gaussian envelope with $\varphi = 0$ and $\nu = 1$.
• Figure 4: Same as Fig. \ref{['fig:MD_betaall_phi0_nu1']} but with $\nu = 5$.
• Figure 5: Ring-like structure in $f_\mathbf{k}(\infty)$ with $k_y = 0$ and $\varphi=0$ for a very long falling edge ($\beta=15$) and a large steepness parameter ($\nu=5$), characteristic of multiphoton pair production. The yellow overlaid circles mark the circular peaks associated with multiphoton absorption and their radii $R$ were determined numerically from the momentum distribution data. The corresponding photon number $n$, obtained from \ref{['eq:multiphoton']} using $|\mathbf{k}| = R$, is not exactly an integer due to the finite pulse duration. No ring-like structure appears for the Sauter envelope as it does not acquire a flat-topped character at large $\nu$ and $\beta$.