We report observation of the signature of very-long-period orbits in the Stark spectrum of lithium in a regime of classical chaos. We identify recurrences associated with the orbits parallel to the electric field, including those beyond the 100th return of the primitive orbit. We also identify recurrences due to scattering of an incoming wave from one orbit into another by the alkali-metal core.PACS numbers: 32.60.+i, 03.65.Sq, 05.45. +b Periodic-orbit theory provides an important link between quantum theory and classical dynamics in regimes of disorderly (chaotic) motion [1]. The closely related closed-orbit theory [2,3] predicts the photoabsorption spectrum of a system from knowledge of its closed classical orbits. Long-period orbits are of particular inter-
We report the results of an experimental and theoretical investigation of the recurrence spectra of Rydberg atoms in a static plus weak oscillating electric field. Experiments reveal the systematic weakening of orbits in a recurrence spectrum as the oscillating field strength and frequency are changed. We describe a generalization of closed orbit theory to time-dependent systems and show that it provides a qualitative and quantitative description of the phenomena. [S0031-9007 (97)03947-1] PACS numbers: 32.60. + i, 03.65.Sq, 05.45. + bIn the quest for a satisfactory understanding of the connections between quantum and classical descriptions of simple Hamiltonian systems, Rydberg atoms in applied fields provide prototypes for experiment and theory [1]. Recurrence spectroscopy and closed orbit theory have proven to be powerful tools for these studies [2][3][4]. A recurrence spectrum is the Fourier transform of a photoexcitation spectrum that is taken with the field varying with energy according to a classical scaling rule that keeps the classical motion unchanged at all points in the spectrum [2]. It can be shown that each closed classical orbit of the electron generates a peak in the recurrence spectrum at the action of the orbit. Consequently, the recurrence spectrum provides a quantum picture of classical behavior. Studies of recurrence spectra have led to observations of the creation of new orbits through bifurcations [5,6], the onset of irregular behavior through core scattering [7-10], symmetry breaking in crossed fields [11], and the identification of numerous closed orbits [1].We have extended this line of inquiry by investigating the recurrence spectrum of a Rydberg atom in a field that is oscillating with a period which is comparable to the period of its classical orbits. The underlying thought is that periodic orbits should be sensitive to periodic perturbations, and that this sensitivity should be revealed by recurrence spectra. Recurrences with periods that are integer multiples of the period of the perturbing field might be expected to be most affected. We report here the first results of such a study. The experimental observations are surprising: Recurrences with periods near integer multiples of the period of the perturbation survive, while those that are out of "resonance" with the field are weakened or eliminated. We have been able to interpret these results by generalizing closed orbit theory to incorporate periodic fields, obtaining both a qualitative and quantitative description of the phenomena.Our study employs a lithium Rydberg atom in a static electric field-a system we have previously studied [8]but now with the addition of an oscillating field. At the low actions studied in these experiments, the spectrum is regular and can be understood by considering only the closed orbits of hydrogen. Experimentally, introducing an rf field is a straightforward task. (We use "rf" to signify the oscillating field though the actual frequency may be in the microwave regime.)
We report an experimental and theoretical study of the effect of bifurcations of closed classical orbits in continuum Stark spectra. Our findings provide a natural way to understand how the spectrum evolves from a simple sinusoidal modulation at positive energy to a quasidiscrete spectrum below the classical ionization limit. The experiment employs scaled-energy spectroscopy of lithium. The results provide the first experimental confirmation of a formulation of closed-orbit theory that provides a quantitative description of the behavior of the spectrum at a bifurcation.
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