An explicit method for the time-dependent Schrödinger Equation: new perspectives for ATI in intense ultra-short pulses and two-photon double ionization |
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| Javier Madronero | |
| Technische Universität München | |
| The study of the quantum dynamics of driven complex atomic systems is a fundamental problem in atomic physics and can be a challenge for both experiment and theory, e.g., the study of strongly correlated two-electron atomic systems driven by short-wavelength or the understanding of tuneling and resonant process in above threshold ionization (ATI) of rare gases. From the theoretical point of view, one of the difficulties is the solution of the time-dependent Schr\"odinger equation (TDSE): explicit integration methods break down when spectral methods are used for the representation of the TDSE. Explicit propagation in the atomic basis -- after full diagonalization of the Hamiltonian -- or the use of implicit methods -- which requires the solution of (large) systems of equations at each integration step -- are the typical solutions to avoid this problem. Both alternatives are numerically demanding in most of the interesting applications. In this contribution we present an alternative ``explicit'' method of 4th order for the stiff TDSE. Taking into account the intrinsic frequencies of the system, the wave function can be expressed in terms of oscillating functions which leads to a simple recursive formula with a controled error. At each integration step only Matrix-vector products are needed. In addition, since the method includes the natural oscillations of the system, the time step is typically large. With help of this method we study single ionization by ultra-short (25fs) 800nm laser pulses at intensities 0.4-1.4 PW/cm$^2$. Pronounced and regular patterns in the electron emission characteristics for single ionization are shown in this tunneling regime (the Keldish parameter is smaller than 0.5). The low-energy part of the photoelectron spectra consists of a series of wide peaks separated by the photon energy, which exhibit features typical for resonantly-enhanced ionization in accordance with experimental observations [1]. [1] Rudenko et al., J. Phys B 37, L407 (2004) |