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Physical Review A

Realistic three-dimensional computations of microwave-ionization curves of hydrogen Rydberg atoms

Graham N. Rockwell, V. F. Hoffman, Th. Clausen, R. Blümel

Published Jan 16, 2002• 4 citations
Publisher

Abstract

We report a realistic computation of experimentally measured microwave ionization curves of hydrogen Rydberg atoms. The experimental field envelope, the duration of the microwave irradiation, the radial droop of the field in the cavity, and the microcanonical distribution of experimental initial states is completely taken into account. We obtain a strong dependence of the ionization probability on the initial magnetic quantum number. Also, a complete 3D three-way comparison between experiment, quantum, and classical theory in the experimentally relevant parameter regime is presented.

DOI
10.1103/physreva.65.025401

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We report a realistic computation of experimentally measured microwave ionization curves of hydrogen Rydberg atoms. The experimental field envelope, the duration of the microwave irradiation, the radial droop of the field in the cavity, and the microcanonical distribution of experimental initial states is completely taken into account. We obtain a strong dependence of the ionization probability on the initial magnetic quantum number. Also, a complete 3D three-way comparison between experiment, quantum, and classical theory in the experimentally relevant parameter regime is presented.
Analytical arguments and numerical simulations suggest that the shapes of 3D microwave ionization curves measured by Koch and collaborators (see P. M. Koch and K. A. H. van Leeuwen, Phys. Rep. {\bf 255}, 289 (1995)) depend only weakly on the angular momentum of the atoms in the initial microcanonical ensemble, but strongly on the principal quantum number and the magnetic quantum number. Based on this insight, coupled with the computational power of a high-end 60-node Beowulf PC cluster, we present the first 3D quantum calculations of microwave ionization curves in the experimentally relevant parameter regime.
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 report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np)2{)}^{2})2P3/2{\mathit{P}}_{3/2}P3/2​(\ensuremath{\Vert}MJ{\mathit{M}}_{\mathit{J}}MJ​\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.
Excitation/ionization probabilities have been measured as a function of microwave electric amplitude F at three different microwave frequencies {omega}/2{pi} = 26.43, 30.36, 36.02 GHz for a wide range of initial no states of hydrogen Rydberg atoms. Using classically scaled variables n{sub 0}{sup 3}{omega}, n{sub 0}{sup 4}F, we discuss the scaling properties of these data. In particular, we note the scaling properties of nonclassical stability observed near n{sub 0}{sup 3}{omega} = 1.3. Our data support the assertion that this stability is due to the presence of a {open_quote}scarred{close_quote} wavefunction.
I show that the theory developed for quantum delocalization of an excited hydrogen atom in a two-frequency linearly polarized microwave field can be used with a few adaptions to explain the quantum delocalization of alkali-metal atoms in a linearly polarized monochromatic field in the regime where it deviates from hydrogenic behavior. Comparison with numerical and laboratory experiments is satisfactory: apart from a constant factor, independent from the microwave frequency, the same dependence from the initial quantum number is observed.