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Physica Scripta

Verification of the validity of the short-pulse approximation for one-dimensional Rydberg atoms

T. Kopyciuk, M Grajek

Published Jul 13, 2011• 0 citations
Publisher

Abstract

In this paper, we investigate the short-pulse approximation (SPA) for one-dimensional Rydberg atoms. We analyse the limits that SPA has to fulfil in order to be applicable. These concern the shape, the duration and the displacement caused by the pulse. The correctness of SPA is tested by comparing the results obtained using SPA with a numerical solution of the set of time-dependent Schrodinger equations. We show that the limit for the displacement caused by the pulse is of greatest importance. Violation of the limit for the duration of the pulse is shown to lead to concurrent violation of the limit for the displacement. We also show that the shape of the pulse has no influence on the created wave packet.

DOI
10.1088/0031-8949/84/02/025301

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In this paper, we investigate the short-pulse approximation (SPA) for one-dimensional Rydberg atoms. We analyse the limits that SPA has to fulfil in order to be applicable. These concern the shape, the duration and the displacement caused by the pulse. The correctness of SPA is tested by comparing the results obtained using SPA with a numerical solution of the set of time-dependent Schrodinger equations. We show that the limit for the displacement caused by the pulse is of greatest importance. Violation of the limit for the duration of the pulse is shown to lead to concurrent violation of the limit for the displacement. We also show that the shape of the pulse has no influence on the created wave packet.
The authors discuss a model excitation of Rydberg wavepackets by short laser pulses. They present an exact non-perturbative solution for a large class of optical pulse shapes. The analysis of exact solutions leads to a formulation and proof of the general approximation scheme (Wigner-Weisskopf-like) valid for arbitrary pulse shapes and a wide range of pulse frequencies, durations and intensities. It is found that the arrangement of the wavefunction depends strongly on the shape of the laser pulse. Coherence of the packet seems to reflect the smoothness of the pulse. Finally, the authors show the equivalence of the saturation processes and the free evolution in the creation of the coherence of the wavepacket, in the case of non-smooth pulse shapes.
Classical, quantum-mechanical, and semiclassical expressions for the transition probability in one-dimensional Rydberg atom irradiated by short half-cycle pulse are derived and compared. The simple formulas obtained for excitation of Rydberg atom by two time delayed weak half-cycle pulses reproduce well the experimental data and the solutions of time-dependent Schr\"odinger equation. When the transferred momenta are stronger and positive, the transition probabilities exhibit fast oscillations with time delay between the pulses. The classical transition probability is constant in time. For negative transferred momenta a focusing phenomenon is observed, and there is a region in time delay, where the transition probabilities oscillate with the Kepler period.
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.
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale inversely with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both three-dimensional classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schr\"odinger equation. More surprisingly, the same scaling behavior in the short pulse limit is also followed by the ionization thresholds for much lower bound states, including the hydrogen ground state. An empirical formula is obtained from a simple model, and the dominant ionization mechanism is identified as a nonzero spatial displacement of the electron. This displacement ionization should be another important mechanism beyond the tunneling ionization and the multiphoton ionization. In addition, an ``ionization window'' is shown to exist for the ionization of Rydberg states, which may have potential applications to selectively modify and control the Rydberg-state population of atoms and molecules.
Summary form only given. A small-area femtosecond pulse propagates in a dispersive medium in a coherent fashion, if the relaxation times of the medium are compared with the pulse length for a long time. As a result, the pulse will be reshaped. This has been described by linear dispersion theory. Using Rydberg states of a molecular or an atomic gas as dispersive medium, the large spectral width of the femtosecond pulse can overlap with more than one level simultaneously. In this case, the shape of the propagated pulse reflects the temporal evolution of the Rydberg wave packet formed by the resonant Rydberg states.
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)].