Semiclassical approximation for strong-laser-field processes
The exact time-evolution operator of an atom in the presence of a strong laser field is expressed using the phase-space path integral. Presenting this result in the form of a perturbative expansion in the effective interaction of the electron with the rest of the atom enables straightforward derivation of the well-known strong-field approximation and its higher-order corrections. Alternatively, one can use this exact result to obtain a semiclassical approximation by expansion in powers of small fluctuations around the classical trajectories. We present a derivation of such a semiclassical approximation. The obtained result for the momentum-space matrix element of the total time-evolution operator can be useful for studying various processes in strong-field physics. Using the example of above-threshold ionization, it is shown how this approximation can be applied to laser-induced processes. More attention is devoted to the laser-assisted scattering. Using the example of few-cycle laser-pulse-assisted electron-atom potential scattering, we show similarities and differences between the semiclassical and the strong-field approximations. For low energies, the semiclassical scattering cross section is modified and there are trajectories along which the electron is temporarily captured by the atomic potential. Applying stationary-phase method to the integral over the scattering time, we clearly identified relevant semiclassical electron trajectories.