The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

TL;DR

This paper explains the oscillatory momentum spectrum observed in vacuum pair production under time-dependent electric fields with sub-cycle laser pulses, by incorporating the Stokes phenomenon into a semiclassical analysis.

Contribution

It introduces a simple quantitative method to incorporate the Stokes phenomenon in analyzing vacuum pair production with complex temporal profiles.

Findings

Explains oscillatory momentum spectra in pair production.

Shows phase differences between spinor and scalar QED.

Provides a semiclassical framework accounting for the Stokes phenomenon.

Abstract

Particle production due to external fields (electric, chromo-electric or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with sub-structure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. Incorporating the Stokes phenomenon, we give a simple quantitative explanation of the recently computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of e+e- pairs produced from vacuum subjected to a time-dependent electric field with sub-cycle laser pulse structure. This approach also explains naturally why for spinor and scalar QED these oscillations are out of phase.