Landau-Zener-St\"uckelberg interferometry in pair production from counterpropagating lasers

TL;DR

This paper investigates electron-positron pair production in counterpropagating lasers using a novel solution to the Dirac equation, revealing interference patterns analogous to Landau-Zener-Stückelberg phenomena in molecular physics.

Contribution

It introduces a new analytical solution to the Dirac equation in this context and demonstrates the occurrence of interference effects in pair production spectra.

Findings

Pair production occurs via non-adiabatic transitions at high laser intensities.

Interference patterns in the pair spectrum are analogous to Landau-Zener-Stückelberg phenomena.

The adiabatic-impulse model accurately describes the interference effects.

Abstract

The rate of electron-positron pair production in linearly polarized counter-propagating lasers is evaluated from a recently discovered solution of the time-dependent Dirac equation. The latter is solved in momentum space where it is formally equivalent to the Schr\"odinger equation describing a strongly driven two-level system. The solution is found from a simple transformation of the Dirac equation and is given in compact form in terms of the doubly-confluent Heun's function. By using the analogy with the two-level system, it is shown that for high-intensity lasers, pair production occurs through periodic non-adiabatic transitions when the adiabatic energy gap is minimal. These transitions give rise to an intricate interference pattern in the pair spectrum, reminiscent of the Landau-Zener-St\"uckelberg phenomenon in molecular physics: the accumulated phase result in constructive or destructive interference. The adiabatic-impulse model is used to study this phenomenon and shows an excellent agreement with the exact result.