We have investigated level statistics in constant-scaled-energy spectra of the diamagnetic helium atom. In a transversely laser-cooled beam metastable triplet atoms are excited to Rydberg states in the presence of a magnetic field, resolving all resonances. In the regime of regular classical motion level distributions obeying Poisson statistics are observed. Small deviations are attributed to scattering at the nonhydrogenic He 1 core as inferred from closed-orbit theory. The nearest-neighbor spacings in spectra in the chaotic regime demonstrate a clear shift towards Wigner statistics. [S0031-9007(98)
We recorded constant scaled-energy spectra of helium Rydberg atoms in both electric and magnetic fields in a regime where the hydrogen atom behaves regularly. Jonckheere, Grémaud, and Delande ͓Phys. Rev. Lett. 81, 2442 ͑1998͔͒ recently showed that the nearest-neighbor statistics of sufficiently highly excited states follows a ␦-Poisson distribution, which depends on the quantum defect ␦. We find global deviations from this ␦-Poisson model, which we attribute to the size of the effective Planck constant ប eff . Significant deviations at small level spacings indicate that the description of level statistics with the ␦-Poisson model is incomplete. ͓S1050-2947͑99͒50409-5͔PACS number͑s͒: 32.60.ϩi, 03.65. Sq, 05.45.Ϫa, 32.80.Rm Quantum systems showing chaotic behavior in the classical limit, sometimes referred to as quantum chaos, are the subject of detailed theoretical and experimental studies ͓1-5͔. Despite impressive progress in the last decade, a profound understanding of the connection between irregular classical dynamics and quantum mechanics is still lacking. The hydrogen atom in a magnetic field is a prototype system to study this chaotic behavior. The classical dynamics in a constant magnetic field undergoes a smooth transition from regular motion to chaos when the energy is raised up to the ionization limit. Experiments on Rydberg atoms and quantum R-matrix calculations have been used to search for quantum manifestations of chaos. Numerical investigations have revealed a relation between quantum-level statistics and the underlying classical dynamics. Nearest-neighbor spacings ͑NNS's͒ in spectra in the regular regime follow a Poisson distribution, while in the chaotic regime they obey a Wigner distribution ͓6͔. A second connection between energy levels in an absorption spectrum and the classical dynamics of the atom has been provided by closed-orbit theory ͓7͔. According to this theory each electron orbit that starts at and returns to the nucleus shows up as an oscillation in the photoabsorption spectrum.
We measured a series of spectra of diamagnetic helium under fixed classical conditions. We varied the scaled energy from ϭϪ0.40 to Ϫ0.26 in steps of 0.02, which corresponds to a gradual increase of the number of chaotic orbits in classical phase space. The classical dynamics of the system is studied using closed-orbit theory. The high resolution of the experiment allows for an investigation of the evolution of the V 1 1 orbit and its repeated traversals. Taking only this stable orbit into account, we reconstruct the most pronounced peaks in the energy spectrum recorded at ϭϪ0.36. The accuracy of our experiment, confirmed by agreement with quantum helium calculations of action spectra up to scaled action 25, provides a good testing ground for recently developed uniform semiclassical approximations in closed-orbit theory. ͓S1050-2947͑99͒07412-0͔
We studied the diamagnetic helium atom under conditions of constant scaled energy over an extended range of Rydberg levels (nϭ77Ϫ160). Experimental spectra are compared with extensive quantum calculations. In the studied range the effective Planck constant ប e varies a factor of 2 ͑from 0.01 to 0.005͒. When comparing Fourier-transformed spectra in different ប e regimes, the resulting action spectra show a large similarity, in accordance with the invariance of the classical dynamics. Prominent variations in the recurrence strength of peaks in the action spectra with ប e could be attributed to interferences between orbits with nearly the same scaled action. In particular, the predicted difference in ប e scaling of the orbit parallel to the magnetic field when compared with the off-axis orbits is confirmed experimentally. ͓S1050-2947͑99͒00509-0͔
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