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Acta Physica Polonica A

Use of Bersons-Kulsh Form Factor of Short-Pulse Approximation in Rydberg-State Physics

R. Parzyński, Michał Sobczak

Published Jan 1, 2003• 1 citation

Abstract

of P hy si cs, A. Mi cki ewi cz Uni versi ty U multowsk a 85, 61-61 4 Po zna¥, Pol an d ( Recei ved Sept ember 10, 2002)T h e exp eri men ts on hi gh R y dberg states intera cting w ith short electromagnetic pulses were hitherto mainly explain ed by using numerical integration of the time-dependent Schr odinger equation in a restricted state basis.I n this study w e apply a di˜erent approach based on the Bersons { K ulsh analytica l form factor of the short-pulse approximation.T his analyti cal approach is show n to w ell repro duce the recent exp erimental results and those of numerical integration of the time-dependen t Schr odinger equation both in the case of terahert z half -cycle pulses and optical many-cycle pulses.T his fact enables a recommendation of the analytical Bersons{K ulsh form factor as an alternati ve and e£cient metho d of quantum calculatio ns of electromagneticall y induced Rydb erg state redistrib uti on.

DOI: 10.12693/aphyspola.103.13

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of P hy si cs, A. Mi cki ewi cz Uni versi ty U multowsk a 85, 61-61 4 Po zna¥, Pol an d ( Recei ved Sept ember 10, 2002)T h e exp eri men ts on hi gh R y dberg states intera cting w ith short electromagnetic pulses were hitherto mainly explain ed by using numerical integration of the time-dependent Schr odinger equation in a restricted state basis.I n this study w e apply a di˜erent approach based on the Bersons { K ulsh analytica l form factor of the short-pulse approximation.T his analyti cal approach is show n to w ell repro duce the recent exp erimental results and those of numerical integration of the time-dependen t Schr odinger equation both in the case of terahert z half -cycle pulses and optical many-cycle pulses.T his fact enables a recommendation of the analytical Bersons{K ulsh form factor as an alternati ve and e£cient metho d of quantum calculatio ns of electromagneticall y induced Rydb erg state redistrib uti on.

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 have ionized Rydberg atoms using subpicosecond half-cycle electromagnetic pulses. The threshold electric field required to ionize a Rydberg state with effective quantum number

{\mathit{n}}^{\mathrm{*}}

is found to scale as ${\mathit{n}}^{\mathrm{*}\mathrm{\ensuremath{-}}2}$ for states with

{\mathit{n}}^{\mathrm{*}}

>13 in contradistinction to the ${\mathit{n}}^{\mathrm{*}\mathrm{\ensuremath{-}}4}$ threshold scaling for static field ionization and high order multiphoton ionization. This novel result is explained using a classical model.

The previously derived approximation for an atom in time-dependent electric fields [P. Krsti\ifmmode \acute{c}\else \'{c}\fi{} and Y. Hahn, Phys. Rev. A 48, 4515 (1993)] is improved for electric pulses of both short and long duration. The transitions that involve a distorted continuum are studied in detail, and the phenomenon of momentum coherence is shown to greatly enhance the transition amplitudes. A detailed comparison with the recent experiment of Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] is presented, where a half-cycle high-power laser pulse was used to ionize Rydberg atoms.

Ionization of Rydberg atoms by short, half-cycle electrical pulses is investigated experimentally in the intermediate-pulse duration regime where the ionization threshold fields are determined both by the slew rate of the ionizing pulse and its duration. Electrical pulses with durations ranging from 140 ps to 9 ns and amplitudes up to are applied to rubidium and lithium atoms prepared in high Rydberg states by laser excitation (n ranges from 42 to 82). The amplitude of the 140 ps pulse required for ionization of the Rb and Li Rydberg population is found to be a factor of two higher than the expected amplitude based on diabatic field ionization and recent theoretical calculations by Reinhold et al (1993 26 L659). Using the longer pulses we studied the transition from the diabatic/adabatic ionization towards ionization in the impulse-kick regime.

A. Mi cki ewi cz Uni versi ty U multowsk a 85, 61-61 4 Po zna¥, Pol an d ( Recei ved Ma y 14, 2003) A m et hod of l inear equation s is prop osed allo win g a redu ction of a ph ysical pro blem of determination of energy , entropy , or magnetisati on for the systems w ith fro zen disorder to a mathematical problem of solvin g a set of linear equations .A part from an exact metho d for determination of energy and entropy , a typ e of the mean Ùeld approach is presented, which p ermits a summation over series representing entropy .Moreo ver, it was establishe d that magnetisati on can app ear only w hen the antif erromagnetic integrals occur at the zero probabil ity .PAC S numb ers: 05.50.+ q, 75.10.N r, 75.50.L k