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Journal of the Optical Society of America B

One-photon resonant two-photon excitation of Rydberg series close to threshold

G. Alber, P. Zoller, Th. Haslwanter

Published Dec 1, 1988• 9 citations
Publisher

Abstract

We study one-photon resonant two-photon excitation of autoionizing Rydberg series close to threshold. Analytical expressions for the time evolution of bound-state amplitudes are derived by adapting ideas from quantum-defect theory. We discuss in detail the two limiting cases of excitation of Rydberg wave packets and ac-Stark splitting close to the threshold.

DOI
10.1364/josab.5.002439

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We study one-photon resonant two-photon excitation of autoionizing Rydberg series close to threshold. Analytical expressions for the time evolution of bound-state amplitudes are derived by adapting ideas from quantum-defect theory. We discuss in detail the two limiting cases of excitation of Rydberg wave packets and ac-Stark splitting close to the threshold.
We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.
The first detailed observation of the perturbations by an electric field of the Rydberg autoionizing resonances of a rare-gas atom is reported. The Stark spectroscopy of autoionizing Rydberg states converging to the second ionization limit $4{p}^{5}^{2}P_{\frac{1}{2}}^{o}$ in Kr I is performed in an atomic beam with the use of a two-step laser excitation from the 4p55s[32]204{p}^{5}5s{[\frac{3}{2}]}_{2}^{0}4p55s[23​]20​ metastable state. In addition to the verification of the ${({n}^{*})}^{\ensuremath{-}3}$ dependence of the zero-field width of two autoionizing series and of the linear dependence of the Stark-manifold splittings with the electric field, we have observed an (n)0.7{(n)}^{0.7}(n)0.7 law for the dependence of the Stark-manifold splitting along the series, an important narrowing and dissymmetrization of the $n{d}^{\ensuremath{'}}$ resonances, and a nonlinear-field behavior of Stark-manifold components in the vicinity of the first anticrossing. Discussions are carried out with the use of the recent work on Rydberg-Stark spectroscopy and on autoionizing states in two-electron atoms.
We present a general method for calculating two-photon processes in real atoms by a variant of the usual multichannel quantum-defect theory (MQDT). Most notably, this method enables us to describe processes in which a single photon has enough energy to ionize the atom (above-threshold processes). All effects of intermediate Rydberg series, continua, or autoionizing series are treated on an equal footing and with the same ease; the final state is also treated properly by standard MQDT. This method should also work for many three- or four-photon processes.
We present a theoretical analysis of a recent experiment [ J. Opt. Soc. Am. B6, 1513 ( 1989)] on two-color three-photon ionization of Xe through resonant even-parity Rydberg states. We calculate second-order ac-Stark shifts, two-photon Rabi frequencies, and ionization widths by using wave functions obtained from a multichannel quantum-defect-theory analysis of the Rydberg series in Xe. We perform a detailed description of the experiment, using the density-matrix formalism, accounting for the temporal and spatial distributions of the laser fields. The agreement with the experiment is good except for the ac-Stark shift of the Rydberg states, which, in our calculation is close to the ponderomotive energy, whereas in the experiment it is measured to be half of this value.
Coherent four-photon scattering of light due to excited and autoionizing states of atomic systems is considered. We analyze the influence of one-photon resonances at the frequency of the anti-Stokes signal and at the frequency of the pump wave on the shape of the spectrum of four-photon scattering. We derive analytical expressions for the line shapes of four-photon scattering involving one-photon resonances with allowance for phase-matching conditions and variation in the populations of excited states for limiting regimes of tight focusing and strong absorption in a medium with a cubic nonlinearity. The calculated spectra of four-photon scattering include the interference of resonant and nonresonant components of the third-order nonlinear susceptibility with allowance for one-photon saturation. We develop a method for normalizing experimental spectra of four-photon scattering with one-photon resonances that takes into account distortion of spectral lines due to the influence of phase mismatch and one- photon absorption.
Three-photon ionization is measured as the frequency of an optical pulse is tuned through two-photon resonance with the Rydberg series of potassium. When the intermediate Rydberg resonance is far below the ionization threshold, the standard resonance profile indicates the enhancement due to a single isolated level. However, as the frequency is tuned closer to threshold, continuous behavior is reached because of the coherent bandwidth of the short pulse and power broadening of the bound-bound transition line. Between these two limiting regions a transition region is observed where discrete and continuous features are manifested. The discrete nature is seen through resonance peaks that blend together as the threshold is approached. The continuous nature manifests itself through the creation of a coherent superposition state that produces localized radial motion. The laser pulse effectively probes the radial orbital motion of this wave packet. Since the ionization rate is drastically reduced while the wave packet is far from the core, drops in the ion signal are seen when the number of times the wavepacket can return to the core is reduced by one. These drops are abrupt because the electron travels much faster near the core in these highly elliptical orbits.