PHYSICAL REVIEW A VOLUME 47, NUMBER 2 FEBRUARY 1993 Dynamical stabilization of atoms in intense laser pulses accessible to experiment Etienne Huens and Bernard Piraux Faculte des Sciences, Unite de Physique Atomique et Moleculaire, Universite Catholique de Louvain, 2 chemin du Cyclotron, B-1348 Louvain-La-fleuve, Belgium (Received 29 June 1992) We analyze the excitation of atoms by intense pulsed laser fields and describe a mechanism leading to effective dynamical stabilization at a photon energy below the unperturbed binding energy. At low and intermediate intensities, the atom is left in a coherent superposition of the initial state and a set of Ryd- berg states which is stable against ionization; this effect subsists for pulse durations presently accessible to experiment. At higher intensities, population is transferred through degenerate Raman coupling to Rydberg states of higher angular momentum. PACS number(s): 32.80.Rm, 42. 50.Hz With the present development of superintense subpi- cosecond pulsed lasers, it is now possible to study the response of an atom exposed to an electromagnetic field which is of the same order or exceeding the electron binding field. Under this condition of strong field, the atom-laser interaction has a highly non-perturbative character which leads to unexpected new effects. Among them, atomic stabilization is probably the most striking and is presently at the origin of many interesting debates. In the high-frequency regime, i.e. , for photon energies substantially higher than the unperturbed ionization po- tential, Floquet theory [1] predicts that for sufficiently high fields, atomic hydrogen becomes stable; in other words, its decay by ionization is quenched. Although several interpretations of this phenomenon exist [2], one usually associates this high-frequency stabilization to a laser-induced delocalization, the so-called dichotomy in the atomic wave function [3]. Whether or not this effect is observable is one of the most fundamental questions. In order for the atom to undergo stabilization, it must survive the low intensities present in the tail of the pulse and for which rapid ionization may occur. Several theoretical studies [4] taking into account the finite turn- on of the pulse and based on the numerical solution of the time-dependent Schrodinger equation demonstrate that high-frequency stabilization does occur. It is clear, how- ever, that with the current laser technology, it is only when the atom is initially in a state with high magnetic quantum number that this effect is observable [5]. High-frequency stabilization of a Rydberg atom may also result from the sharp turn-on of the pulse [6]. In this case, the finite bandwidth of the laser pulse overlaps several initially unpopulated Rydberg states; these states are pumped through Raman coupling with the continu- um into a coherent superposition which is stable against ionization. The Rydberg state degeneracy as well as the coupling of these Rydberg states with a low-lying state do not play, in this case, a significant role [7]. By contrast to the previous stabilization process, the present one, which is sensitive to the pulse shape and which involves many atomic states during its time evolution, is usually referred to as dynamical stabilization. Experimental evidence for redistribution of Rydberg state population by an intense short laser pulse exists [8]. However, if, in a realistic situ- ation, the stabilization of a Rydberg atom does occur, both previous mechanisms are effective [9]; whether or not it is possible to clearly define the specific role of each of them is still an open question. In this Brief Report, we demonstrate that with the present (aser technology, effective dynamical stabilization should be also observable for photon energies below the unperturbed ionization potential. This stabihzation re- sults from two distinct processes. For electric-field strengths less than or equal to the atomic field, i.e. , in the tail of the laser pulse, the atom is left in a coherent super- position of the initial state and a set of Rydberg states which is stable against ionization. Here, we show that for various frequencies, this coherent process subsists for pulse durations exceeding 100 fs. It must be stressed that in this case, the Rydberg wave packet is not the result of a direct short pulse excitation from a compact low-lying state; instead, its formation, far from the nucleus, stems from extended high-lying states which are accessed virtu- ally through Raman coupling [10]. For electric-field strengths higher than the atomic field, part of the popula- tion is transferred through degenerate Raman coupling to excited states of higher angular momentum. In other words, several new Rydberg wave packets are created. Being characterized by a high angular momentum, the overlap of these wave packets with the nucleus is expect- ed to be very small and as a result, the effective interac- tion with the field to be very weak. In order to illustrate this stabilization mechanism, we consider the interaction of a short laser pulse with atomic hydrogen initially in the 2s state. The interaction Hamil- tonian is expressed in its velocity form and the vector po- tential associated to the laser pulse is defined as follows: A(t) = Ao exp[ — (tlat) ] sin(cot ), where cu is the laser frequency and ~ a parameter which fixes the width of the Gaussian envelope. We solve the corresponding time-dependent Schrodinger equation by using a spectral method. After a complex rotation of the 1568 1993 The American Physical Society