Wave-packet analysis of laser-induced half-collision processes

Abstract

The usual approach to calculating multiphoton collision and half-collision processes uses the interaction picture and introduces a classical time-dependent field into the Hamiltonian for the scattered particles, which is further simplified using the Floquet ansatz. In particular, the laser-induced decay of an initial bound state is derived from a half-collision loquet ansatz that utilizes a complex quasienergy, whose imaginary part is identified with the laser-induced decay constant of the bound state. This interpretation presupposes a pure exponential decay of the initial-state population and yields a Lorentzian distribution of product-state energies in the infinite-depletion limit. Here we demonstrate how a full-collision Floquet ansatz can be derived from a fully quantal wave packet constructed to represent scattering in the presence of a coherent state of the laser field. The wave packet utilizes the set of the time-independent close-coupled wave functions for scattering in the field generated by quantized radiation number states. The resultant Floquet scattering states are energy normalized and stationary, and the quasienergy is real. We show how to use these states to construct a coherent-state wave packet that describes the decay of an arbitrarily prepared bound state, and yields a half-collision Floquet ansatz without any commitment to a complex quasienergy. The product energy and quantum-state distribution in the infinite-depletion limit are obtained without approximation to exponential decay. Further we show how the Fourier transform of the infinite-depletion line shape gives the temporal behavior of the initial bound-state population, often with distinctly nonexponential behavior. Such results are demonstrated for the above-threshold ionization of H, and the above-threshold dissociation of ${\mathrm{H}}_{2}^{+}$. In the following paper [R. W. Heather and F. H. Mies, Phys. Rev. 44, XXXX (1991)], excellent agreement is found between the present fully quantal wave-packet approach, utilizing the time-independent scattering wave functions, and the comparable solutions to the time-dependent Schr\"odinger equation for a corresponding classical time-dependent laser field.