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arXiv · 1207.4742

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

François Fillion-Gourdeau·Emmanuel Lorin·André D. Bandrauk
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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.

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François Fillion-Gourdeau, Emmanuel Lorin, André D. Bandrauk. 2012-07-19. Landau-Zener-St\"uckelberg interferometry in pair production from counterpropagating lasers. https://doi.org/10.1103/physreva.86.032118

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