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Laser Physics

Pulse-duration dependence in the theory of interference stabilization of Rydberg atoms

С. М. Федоров, Olga V. Tikhonova, Mikhail Vladimirovich Fedorov

Published Jan 1, 2000• 2 citations
OpenAlex

Abstract

The phenomenon of interference stabilization of Rydberg atoms is studied. The residual probability W res of finding an atom in bound (Rydberg) states and the threshold of stabilization V thr are calculated in their dependence on the pulse duration τ (for pulses with smooth envelopes). At τ longer than the Kepler period t K , both W res (τ) and V thr (τ) are shown to oscillate with approximately the Kepler period. At τ < t K (the case often referred to as transient stabilization), the threshold of stabilization V thr (τ) is shown to be a growing function of a decreasing pulse duration τ. Transient stabilization is shown to be explained by the same physical reasons as interference stabilization, and this implies that the concept of interference stabilization can be used in both limits of long and short pulses.

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Physical Review A•Mar 1, 1994•26 citations
The phenomenon of interference stabilization of Rydberg atoms is studied. The residual probability W res of finding an atom in bound (Rydberg) states and the threshold of stabilization V thr are calculated in their dependence on the pulse duration τ (for pulses with smooth envelopes). At τ longer than the Kepler period t K , both W res (τ) and V thr (τ) are shown to oscillate with approximately the Kepler period. At τ < t K (the case often referred to as transient stabilization), the threshold of stabilization V thr (τ) is shown to be a growing function of a decreasing pulse duration τ. Transient stabilization is shown to be explained by the same physical reasons as interference stabilization, and this implies that the concept of interference stabilization can be used in both limits of long and short pulses.
Photoionization of Rydberg atoms is considered in the framework of the quasiclassical (WKB) approach. Distribution of the photoelectron density in space and time is found and analyzed. This distribution is shown to consist of two main parts: the temporary population, which exists only as long as the light field is on; and the population corresponding to irreversible ionization. The irreversible-ionization wave packets are shown to experience the effect referred to as Coulomb narrowing. An origin of this effect and the conditions of its existence are discussed. In a strong field, rather simple analytical expressions are found for the partial probabilities of above-threshold ionization and for the total probability of ionization. In contrast to many earlier works, in the present theory neither the rotating-wave nor ``pole'' approximations are used, and the results are derived for an arbitrary pulse shape. Strong-field interference stabilization of Rydberg atoms is confirmed to occur at pulse durations shorter than the Kepler period. The arising regimes of interference stabilization are analyzed in comparison with the predictions of earlier works.
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.
Interference stabilization of atoms is investigated numerically. Raman-type transitions to Rydberg states with higher values of the electron orbital momentum are taken into account. These transitions are shown to change qualitatively theoretical predictions concerning the dependence of the time of ionization on the light-field-strength amplitude : if the weak-field time of ionization, as usual, is a falling function of , in a strong-field region the function is predicted to be more or less constant and of the order of the classical Kepler period in a rather large interval of , in contrast with the earlier prediction according to which, in a strong field, was assumed to be a rather fast growing function. The results derived are shown to be in a rather good agreement with the existing experiments. Alternative theoretical models are discussed.
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 describe the results of our solutions of the time-dependent Schr\"odinger equation for Rydberg states of atomic hydrogen exposed to a short pulse of ``half-cycle'' long-wavelength radiation. By ``short'' we mean that the duration of the pulse is much less than the Kepler period of the Rydberg state being irradiated. Comparison is made with the results of experiments which have been reported recently [R. Jones, D. You, and P. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993)].