We have measured the microwave ionization threshold electric fields for ns-state Na Rydberg atoms from n=24--33 as a function of the duration of the ionizing microwave pulse. Pulses as short as 2.8 ns were used, containing fewer than 25 cycles of 8.55-GHz radiation. While the fields required to produce the onset of ionization were independent of pulse duration and exhibited the ${\mathit{n}}^{\mathrm{\ensuremath{-}}5}$ scaling characteristic of ionization by diffusion through higher-energy states, the fields required to produce nearly complete ionization increased dramatically as the pulse was shortened. Additional measurements of the populations of bound states after the shortest microwave pulses showed that up to \ensuremath{\sim}10% of the atoms were excited to states above the initially populated ns state and the adjacent (n-1) manifold of higher angular momentum states, while most either ionized or remained in these states. From this observation we conclude that the rate-limiting process for ionization is the transition from the initially populated ns states or the adjacent manifold to the next higher manifold, not the diffusion through higher-lying states.
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.
Ionization of Rydberg atoms by short, half-cycle electrical pulses is investigated experimentally in the intermediate-pulse duration regime where the ionization threshold fields are determined both by the slew rate of the ionizing pulse and its duration. Electrical pulses with durations ranging from 140 ps to 9 ns and amplitudes up to are applied to rubidium and lithium atoms prepared in high Rydberg states by laser excitation (n ranges from 42 to 82). The amplitude of the 140 ps pulse required for ionization of the Rb and Li Rydberg population is found to be a factor of two higher than the expected amplitude based on diabatic field ionization and recent theoretical calculations by Reinhold et al (1993 26 L659). Using the longer pulses we studied the transition from the diabatic/adabatic ionization towards ionization in the impulse-kick regime.
The 38-GHz microwave field required to effect 50
ionization of Li atoms decreases from 60 V/cm at
n=37, where the microwave frequency is one-third the Kepler frequency, to 45 V/cm at
n=56, where the microwave frequency is equal to the Kepler frequency. For
n>56 the 50
ionization field is constant at $E\ensuremath{\approx}2.4{\ensuremath{\omega}}^{5/3}$ until $\ensuremath{\sim}80$ GHz below the ionization limit, where it begins to decline. In spite of the fact that the pulse is 8000 cycles long, we detect approximately 5
of the initial population in very-high-lying (
n>215) states subsequent to the microwave pulse. We suggest that these atoms are trapped in metastable atom-field states during the microwave pulse and relax to the high-lying states when the field is turned off. The existence of such states is predicted by the simple man's model of above-threshold ionization.
Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The
∣m∣=0and1 states may be ionized with a very low microwave field, $\ensuremath{\sim}\frac{1}{{3n}^{5}}$, corresponding to the point at which the
n and
n+1 Stark manifolds of principal quantum numbers
n and
n+1 intersect. The ionization occurs by an atom's making a succession of Landau-Zener transitions to higher-lying states, finally reaching the classical ionization limit. The
∣m∣=2 states, on the other hand, ionize at a very high microwave field, $\ensuremath{\sim}\frac{1}{{9n}^{4}}$. Both these observations and the more familiar static or low-frequency result of ionization by a field of $\ensuremath{\sim}\frac{1}{{16n}^{4}}$ are all consistent with ionization in a completely classical fashion. The apparent differences are due to the dynamics of passing from zero field to a high ionizing field.
We report microwave ionization experiments with Rydberg states of Na using several microwave frequencies near 80 GHz. We observe substantial ionization of states as low as
n=26 with microwave pulses of 170-V/cm amplitude. Unlike experiments at 38 and 17 GHz, microwave ionization is not always accompanied by the production of the extremely high-lying states just below the limit. It only occurs when the initial Rydberg state is in multiphoton resonance with the high-lying states. The resonance condition is apparent at 80 GHz because the ponderomotive energy shift of the limit, and of the high-lying states, is small compared to the microwave frequency, even at fields strong enough to produce ionization. At the lower microwave frequencies, the ponderomotive shift exceeds the microwave frequency, ensuring that the resonance condition is met and obscuring its importance. The same is true of many laser experiments.