The inverse problem for Schwinger pair production

TL;DR

This paper demonstrates how quantum kinetic and optimal control theories can be combined to solve the inverse problem of designing electric fields that produce desired electron-positron momentum spectra in Schwinger pair production, aiding experimental observation.

Contribution

It introduces a novel approach using quantum kinetic and optimal control theories to approximately solve the inverse problem in Schwinger pair production.

Findings

Successfully designed field configurations for target momentum signatures

Showed the method's potential to guide experimental setups

Illustrated the approach with superpositions of harmonic components

Abstract

The production of electron-positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.