The primary goal of research in "quantum chaos" is to explore the extent to which the methods and natural intuition of classical mechanics can be used to elucidate the complex and often surprising behavior of large quantum systems. Much recent work is based on the deep connections between classical periodic ͑or closed͒ orbits and the quantum spectrum revealed by semiclassical "trace formulas." These ideas have important applications in the analysis of the "recurrence spectrum" of Rydberg atoms

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... n strong static electric fields in which the measured peaks are associated with individual classical periodic orbits. Here we present detailed experimental measurements of the recurrence spectrum for nϭ15-25, singlet and triplet, mϭ0, 1, helium Rydberg atoms and we provide a purely quantum-mechanical explanation for the structure of the recurrence spectrum based on the regularities of the Stark photoabsorption spectrum. This analysis serves to demystify these ͑still complex͒ representations of the quantum spectrum; provides new insight into the functional differences between hydrogen and helium Rydberg atoms in strong fields; and reemphasizes the remarkable correpondence between the classical and quantum theory for these systems.