We have studied the ionization of Na ns and nd Rydberg atoms by \ensuremath{\sim}1-\ensuremath{\mu}s pulses of 10-MHz, 670-MHz, 2-GHz, and 4-GHz fields, bridging the gap between the previous measurements of ionization by \ensuremath{\sim}1-\ensuremath{\mu}s rise-time pulses and 8- and 15-GHz microwave fields. We have also studied the ionization of Li ns and nd Rydberg atoms by 4-, 8-, and 15-GHz fields, which, due to the smaller Li quantum defects, represents the high-frequency limit of nonhydrogenic microwave ionization. The Na measurements show that ionization at 10 MHz occurs without change in n at fields of 1/16
n4 and 1/9
n4. At 670 MHz \ensuremath{\Vert}m\ensuremath{\Vert}=0, 1, and 2 states are all ionized at fields between 1/3
n5 and 1/9
n4, indicating that transitions to higher-n states are occurring. As the frequency is raised further, to 2 and 4 GHz, the \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states exhibit an increasingly sharp threshold for ionization at E=1/3
n5, but the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states are unlikely to ionize at this field, with ionization occurring mostly at higher fields, 1/3
n5E1/9
n4, approaching the 15-GHz behavior of ionization at E=1/9
n4. At 4 GHz, Li n=20 \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states ionize at E=1/3
n5, but at n\ensuremath{\simeq}45, \ensuremath{\Vert}m\ensuremath{\Vert}=1 states ionize at E=1/9
n4, and the \ensuremath{\Vert}m\ensuremath{\Vert}=0 states ionize at E>1/3
n5. The \ensuremath{\Vert}m\ensuremath{\Vert}=2 states appear to ionize at E=1/9
n4. As the frequency is raised to 8 and then to 15 GHz, the transition of \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states to ionization at E=1/9
n4 occurs at lower n. When a small static field is applied, the Li ionization threshold fields drop from 1/9
n4 to fields somewhat above 1/3
n5. Together the Na and Li measurements show that microwave ionization depends on a rate-limiting step, which is a resonant multiphoton transition.
We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np
)2P3/2(\ensuremath{\Vert}
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.
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.
Near threshold the microwave ionization rates of Na \ensuremath{\Vert}m\ensuremath{\Vert}=0,1 Rydberg states within a Stark manifold n show a strong dependence on the location of the state within the manifold. In particular, the rate-limiting step for ionization of states with the smallest Stark shifts (\ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\ll}n) is different from the field-limited step of making the n\ensuremath{\rightarrow}n+1 transitions at threshold fields
FT\ensuremath{\simeq}1/3
n5 (a.u.). This variation in the ionization rates as a function of manifold location or Stark shift may be understood in terms of the variation in the transition probability to the bluest Stark states from the other members of the manifold.