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AIP conference proceedings

Ionization and excitation of hydrogen and helium Rydberg atoms by microwaves

Leo Moorman, B. E. Sauer, Suzanne Yoakum, Patrick M. Koch, Enrique J. Galvez, Willem van de Water, K. A. H. van Leeuwen

Published Jan 1, 1990• 1 citation

Abstract

We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.

DOI: 10.1063/1.39175

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Physical Review Letters•Sep 28, 1992•56 citations

We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited

{\mathit{n}}_{0}

^{3}

S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range

{\mathit{n}}_{0}

=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of

{\mathit{n}}_{0}

^{3}

S\ensuremath{\rightarrow}

{\mathit{n}}_{0}

^{3}

L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the

{n}^{3}

S to

{n}^{3}

(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.

Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.

A numerical method is presented to treat atoms in strong time-dependent electric fields. The method is applied to calculate ionization probabilities of H Rydberg atoms in strong monochromatic and bichromatic microwave fields. Recent experimental data on the microwave ionization of H Rydberg atoms are well reproduced. Ionization probabilities for microwave field parameters not yet covered experimentally are predicted. We propose to use the setup of existing two-frequency waveguide experiments to reveal the structure of the quasi-energy spectrum of microwave-driven Rydberg atoms. In analogy to dressed-state spectroscopy of atoms in strong laser fields, the quasi-energies of a periodically driven quantum system are mapped out by sweeping the frequency of a second (weak) additional rf probe field.

We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28)

^{3}\mathrm{S}

Rydberg atoms. They are produced by the coherent evolution along two isolated Floquet potential curves as the microwave electric field amplitude varies along a half-sine-wave pulse shape. The measured visibility and separation of the oscillations depends sensitively on the Floquet structure, on the atomic beam velocity, and particularly on additive noise, which smears and broadens the pattern.