Electron delocalization and transfer induced by a time-dependent potential: Exact treatment of a simple model — delocalization

We study the delocalization of a quantum particle in a one-dimensional, short-range (δ function), time-dependent potential. The energy spectrum of the emitted particle and the transition probability per unit time are obtained numerically by solving the Lippman–Schwinger equation using the discretized fractional calculus method of Lubich. An analytical calculation that follows the lines of the Keldysh–Faisal–Reiss treatment of the closely related problem of high-intensity laser-induced multi-photon ionization of atoms is also presented. As in this latter case, we observe an above-threshold ionization and a ponder-omotive shift associated with the emitted particle energy spectrum. The transition probability per unit time, as calculated analytically, is found to agree well with the numerical results for small enough perturbations. As the amplitude or the frequency of the excitation is varied, a feedback mechanism between the various ionization channels is observed.