Relativistic effects in the time evolution of a one-dimensional model atom in an intense laser field

Abstract

Using a B-spline expansion in momentum space, we have solved the time-dependent Dirac equation numerically for a model, one-dimensional atom which is subjected to an ultra-intense, high-frequency laser field. We find that for a peak electric field strength of 175 atomic units (au) and for angular frequencies of 1 and 2 au, relativistic effects start to become apparent. Even under these extreme conditions the wavefunction remains localized in a superposition of field-free bound states and very-low-energy continuum states. Comparing our results with the numerical solution of the time-dependent Schrödinger equation, we find that the Dirac wavefunction is slightly more stable against ionization. We also find that the energy distribution of the ionized electrons is strongly concentrated near threshold and that a cut-off in the high-energy spectrum occurs at the energy corresponding to the maximum momentum of a classical electron in the laser field.