Tracking quantum-cloud expansion in tunneling ionization

We study the formation and evolution of the electron wave packets in the process of strong-field ionization of various atomic targets. Our study is based on reformulating the problem in terms of conditional amplitudes, i.e., the amplitudes describing outcomes of measurements of different observables provided that the electron is found in the ionized state after the end of the pulse. By choosing the electron coordinate as such an observable, we are able to unambiguously define the notion of the ionized wave packets and study their formation and spread. We show that the evolution of the ionized wave packets obtained in this way closely follows the classical trajectories at the initial stages of evolution providing an ab initio quantum mechanical confirmation of the basic premises of the classical Monte Carlo calculations approach. At the later stages of evolution, the picture becomes more complicated due to the wave packets' spread and due to interference of wave packets originating from different field maxima. Our approach also allows us to obtain information about the coordinate and velocity electron distributions at the tunnel exit.