Entropic measure of wave-packet spreading and ionization in laser-driven atoms.

Abstract

We consider wave-packet spreading and ionization of a one-dimensional model hydrogen atom interacting with a strong high-frequency laser field in the stabilization domain. We demonstrate the effect of the pulse shape on the dynamics in phase space and visualize our results with both the Wigner and the Q function phase-space quasiprobability representation. The Wehrl entropy is introduced and utilized as a convenient one-parameter measure of wave-packet spreading, phase-space localization, and ionization. @S1050- 2947~96!02007-0# We therefore also consider a second phase-space distribution function, the Husimi or Q representation @10#, which is al- ways positive. The Husimi distribution can be used to calcu- late an information-theoretic measure of the number of par- ticipating quasiclassical Gaussian wave packets. This measure is the Wehrl entropy @11# and, apart from interfer- ence terms, is determined by the number of Gaussian coher- ent states to ''tile'' its phase-space contour. The Wehrl en- tropy has been investigated and utilized by a group of authors @12#. It has recently been studied within a wider class of entropies that are based on a comparison of the wave function with an arbitrary basis of states in phase space @13#. This Wehrl entropy is directly related to the uncertainty area of the Q function in phase space and it is appropriate as a measure of wave packet spreading and ionization. We will use the Wehrl entropy to study the effect of these phenomena in the stabilization domain using both an adiabatic sin 2 and a nonadiabatic trapezoidal pulse. In the next section we will describe our numerical model, based on the solution of the time-dependent Schrodinger equation in one dimension. We will then investigate the sta- bilization dynamics for two different pulse shapes ~one adia- batic, the other with a fast turn-on! using the Wigner func- tion, before turning our attention to the Q function and finally to the Wehrl entropy.