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Journal of the Optical Society of America B

Dark-state effect in Rydberg-atom stabilization

Antoni Wójcik, R. Parzyński

Published Mar 1, 1995• 12 citations
Publisher

Abstract

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.

DOI
10.1364/josab.12.000369

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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.
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.
We have observed that the amount of photoionization from an atomic Rydberg state with a pulsed laser depends critically on the length of the pulse, whereas lowest-order perturbation theory implies that the yield depends only on the fluence (the integrated intensity) of the pulse. We have measured the yield for one-photon ionization with short (0.5–2.7-ps) high-intensity laser pulses from the 27d Rydberg state in barium. With equal fluence, the yield decreases for pulses shorter than the Kepler orbit time of the outer electron (2.2 ps) because not all of its wave function comes near the core during the length of the pulse. The observations and this classical picture are confirmed by quantum-mechanical calculations.
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.
We have observed trapping of population in Rydberg states of atoms and ions exposed to intense laser radiation. The trapping occurs in nonstationary ``wave-packet'' superposition states, created, via ac Stark-shifted multiphoton resonances during the laser pulse. The formation of these highly excited bound states requires the nonresonant absorption of up to 20 or more photons; some of the ionic Rydberg states lie nearly 32 eV above the ionic ground state. All of the trapped states having binding energies much less than the photon energy but remain stable against ionization even when the multiphoton ionization probability of the atom is saturated.
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.
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.