Time dependence of an atomic electron wave function in an electrical field

Abstract

We present measurements and calculations of the time-dependent behavior of an electron bound in a Coulomb potential placed in an additional static electrical field. The time-dependent behavior is studied by means of the evolution of a wave packet. The wave packet is created by coherent superposition of several k states of one Stark manifold. It is pointed out that the oscillation of this ``parabolic'' wave packet corresponds to an oscillation of the angular momentum l. In the case of a hydrogen atom the spacing between the k states is constant, leading to a dispersion-free wave packet. For this situation the parabolic wave packet \ensuremath{\Vert}\ensuremath{\Psi}(x,z)${\ensuremath{\Vert}}^{2}$ is plotted as a function of time. The oscillations of the parabolic wave packet can be measured by photoionization, because the photoionization probability is l dependent. The time-dependent photoionization probability is calculated in two steps. First the l-population coefficients are calculated as a function of time. Then we calculated the transition probability of each l state to the continuum. Combining these two allows us to calculate the time-dependent ionization probability. Experimentally, a wave packet is created by coherent superposition of k states of rubidium atoms with a 7-ps laser pulse. The ionization probability is probed by a second laser pulse, which is delayed with respect to the first one. In this way as many as ten oscillations of the parabolic wave packet are observed. The calculations (for hydrogen) agree well with the experimental result of the pump-probe experiment. The ac Stark shift of a k manifold due to the laser field was measured in a separate experiment; the determined value of 0.01 meV/(GW/${\mathrm{cm}}^{2}$) is low enough to ensure that intensity effects can be neglected.