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Physical Review A

Analytical investigation of one-dimensional Rydberg atoms interacting with half-cycle pulses

Imants Bersons, Rita Veilande

Published Apr 20, 2004• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.69.043408

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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.
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)].
We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution.If the momentum (q2) delivered to the atom by the second kick is much smaller than that (q1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom.For q2 ≥ q 1 4 appearance of revival and fractional revival depends on both the values of q2 and time delay t1 between the pulses but more sensitively on t1.The number of fractional revivals tends to become numerous as the value of t1 increases.
The angular and energy distributions of electrons emitted from Rydberg atoms prepared in the extreme Stark state and irradiated by a short half-cycle pulse are calculated in the framework of quantum-mechanical and semiclassical theories. It is supposed that the pulse direction coincides with the direction of orientation of atoms. The emitted electrons are concentrated in a small angle around the direction of orientation of the Rydberg atoms. Semiclassical theory shows that the width of the angular distribution scales as 1/qn3/2 and decreases with increase of either the principal quantum number n of the initial state or the momentum q transferred to the electron.
We discuss the physical sense and interpretation of the Maeda—Gallagher experiment (2004) in which the probability of ionisation of Rydberg Li atoms perturbed by the resonance microwave field by a short half-cycle pulse was measured. The periodic dependence of the ionisation probability w i on the delay time t 0 of the half-cycle pulse with respect to the instant of switching on the microwave field is found. The oscillation period of the function w i ( t 0 ) is equal to the Kepler period of a Rydberg electron. It is shown that the interpretation of this experiment by the authors in terms of localised wave packets has no grounds and neglects basic processes proceeding in the microwave field. An alternative interpretation is proposed and, as the first step, the structure of the Rydberg wave function formed in the resonance microwave field is studied.
We investigate many characteristic features of revival and fractional revival phenomena via derived analytic expressions for an autocorrelation function of a one-dimensional Rydberg atom with weighting probabilities modelled by a Gaussian or a Lorentzian distribution. The fractional revival phenomenon in the ionization probabilities of a one-dimensional Rydberg atom irradiated by two short half-cycle pulses is also studied. When many states are involved in the formation of the wave packet, the revival is lower and broader than the initial wave packet and the fractional revivals overlap and disappear with time.