Landau-Zener-Stuckelberg interferometry in pair production from counterpropagating lasers

The rate of electron-positron pair production in linearly polarized counterpropagating 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 Schrodinger 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 nonadiabatic 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-Stuckelberg 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.