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Physical Review Letters

Effective stabilization of Rydberg states at current laser performances

R. J. Vos, Mihai Gavrila

Published Jan 13, 1992• 96 citations
Publisher

Abstract

Stabilization, the exotic process by which an atom in a superintense laser field, of the order of the atomic unit, reacts to the increase in intensity or decrease in frequency by increasing its lifetime, has been recognized as elusive for atomic ground states. We now show that the stabilization regime can be effectively attained at present laser performances (intensities, frequencies, pulse shapes) when starting with atoms prepared initially in Rydberg states of high magnetic quantum number with respect to the axis of linear polarization.

DOI
10.1103/physrevlett.68.170

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Physical Review A•Sep 1, 1994•17 citations
Stabilization, the exotic process by which an atom in a superintense laser field, of the order of the atomic unit, reacts to the increase in intensity or decrease in frequency by increasing its lifetime, has been recognized as elusive for atomic ground states. We now show that the stabilization regime can be effectively attained at present laser performances (intensities, frequencies, pulse shapes) when starting with atoms prepared initially in Rydberg states of high magnetic quantum number with respect to the axis of linear polarization.
We show that, when an atom prepared in a high Rydberg state is one-photon ionized by a laser, a near resonance with some lower-lying state permits the formation of a nondecaying dark state of the coupled laser–atom system. This dark state traps population in an amount that increases to some upper limit as the laser radiation used becomes stronger. Thus the dark state formed causes a decrease in the Rydberg-atom ionization with increasing laser intensity, i.e., stabilization, which survives even for long times. This long-time stabilization is described by a simple zero-pole formula, and the physical meaning of the term long time is explained. We estimate, for model situations, the laser frequencies that ensure dark-state formation and maximum ionization suppression. The laser pulse intensity and duration that are required for the observation of the dark state are evaluated.
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 Rydberg 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.
Quantitative results are presented for stabilization of atoms against ionization by strong laser fields over a wide range of frequencies for circular and linear polarization. With circular polarization, stabilization occurs for all frequencies. At high frequency (\ensuremath{\omega}>1 a.u.), the stabilization intensity is predicted by the occurrence of photon thresholds. This mechanism gives excellent numerical agreement both with present calculations and the results of Pont and Gavrila [Phys. Rev. Lett. 65, 2362 (1990)]. A different mechanism operates for \ensuremath{\omega}1 a.u. Linear polarization differs strongly from circular polarization in many respects.
An analytical study is presented of two models of intense-laser ionization from an isolated initial state via a band of high-Rydberg states in a system which bears many features of the hydrogen atom. The models differ in the way the population from the directly excited Rydberg states can migrate to the states of higher angular momenta. In one of them it migrates via nonresonant and in the other via resonant degenerate Raman coupling. Within these models we draw conclusions about the efficiency of migration, the initial-state lifetime, the redistribution of population, the laser intensities stabilizing the atom against ionization, the effect of the initial state on the threshold stabilizing intensity, as well as about stabilizing mechanisms versus the initial-state choice.
It is shown that the rate and degree of ionization of an atom can be controlled by preparing a specific superposition of Rydberg states. This effect is due to the Raman interaction of Rydberg levels via resonant lower-lying levels of the atom. Depending on the initial population of an atom interacting with a strong laser field, the atom either ionizes completely or exhibits an extremely high degree of stability (in this case the probability of the atom remaining in a bound state when the laser pulse is switched off is close to 1). It is shown that states which are stable against ionization decay or, conversely, decay rapidly into the continuum can be prepared using double laser pulses with a controllable time delay.
Stimulated by a recent experiment [L. D. Noordam et al., Phys. Rev. Lett. 68, 1496 (1992)], we present a model of Rydberg-atom photoionization whose essential feature is the resonance between the initially populated Rydberg state and an additional state lying below Rydberg quasicontinuum. Despite the infinite number of discrete states involved in our model we have obtained the expressions for photoionization yield and discrete-state populations in completely analytical form. These expressions cover both short- and long-time scales, i.e., when laser-pulse duration is shorter or longer than the classical round-trip time of the Rydberg electron. The short-time scale corresponds to the conditions met in the experiment of Noordam et al. and, on the basis of our expressions, we have gained at least qualitative understanding of their observations. In the case of long pulses, which in our considerations are never longer than 54 ps, near resonance is shown to be the origin of a profound ionization suppression, particularly for some specific frequencies, which we identify as those ensuring the formation of a perfectly dark dressed state of zero width and thus unionizable. This dark state is shown to be populated with a probability increasing when laser gets stronger. We discuss the connection between stabilization and formation of this perfectly dark state as well as of additional dressed states, which are dark in the sense that they have the property of becoming very narrow as laser intensity increases. The undamped perfectly dark state, created at specific laser frequencies, has given us rise to introduce what we call the zero-pole approximation for ionization yield, which, as we have shown, works well if duration and intensity of laser pulse are appropriately combined.