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Journal of Physics B Atomic Molecular and Optical Physics

Excitation of Rydberg wavepackets by short laser pulses

Jan Grochmalicki, Maciej Lewenstein

Published Oct 14, 1988• 8 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/21/19/017

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Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.

Physical Review A•Jan 1, 1999•3 citations
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.
Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.
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 saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.
Atoms in high-lying Rydberg states with large values of principal quantum number n, n ≥300, form a valuable laboratory in which to explore the control and manipulation of quantum states of mesoscopic size using carefully tailored sequences of short electric field pulses whose characteristic times (duration and/or rise/fall times) are less than the classical electron orbital period. Atoms react to such pulse sequences very differently than to short laser or microwave pulses providing the foundation for a number of new approaches to engineering atomic wavefunctions. The remarkable level of control that can be achieved is illustrated with reference to the generation of localized wavepackets in Bohr-like near-circular orbits, and the production of non-dispersive wavepackets under periodic driving and their transport to targeted regions of phase space. New protocols continue to be developed that will allow even tighter control with the promise of new insights into quantum-classical correspondence, information storage in mesoscopic systems, physics in the ultra-fast ultra-intense regime, and non-linear dynamics in driven systems.
Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.