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Physical Review A

Production of extremely-high-lying states in 17-GHz microwave ionization of Li and Na

Alexandr Arakelyan, Thomas F. Gallagher

Published May 14, 2014• 1 citation
Publisher

Abstract

In the ionization of Li and Na by a 16.91-GHz microwave field, roughly 20% of the atoms are not actually ionized but trapped in highly excited states within one or, at most, two microwave photons of the ionization limit. The highly excited atoms appear at the same field as the onset of microwave ionization, irrespective of whether ionization occurs at the field $E=1/3{n}^{5}$ or $E=1/16{n}^{4}$. The highly excited atoms are only detected in static fields less than 35 mV/cm, a field which roughly corresponds to field ionization of an atom bound by twice the microwave frequency. We also show that Na $|m|=1$ atoms require a microwave field of $E=1/9{n}^{4}$ for ionization in zero static field, but the required field for ionization is reduced to $E=1/3{n}^{5}$ if a static field of 1 V/cm is present.

DOI
10.1103/physreva.89.053412

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Physical Review A•Nov 17, 2016•19 citations
In the ionization of Li and Na by a 16.91-GHz microwave field, roughly 20% of the atoms are not actually ionized but trapped in highly excited states within one or, at most, two microwave photons of the ionization limit. The highly excited atoms appear at the same field as the onset of microwave ionization, irrespective of whether ionization occurs at the field E=1/3n5E=1/3{n}^{5}E=1/3n5 or E=1/16n4E=1/16{n}^{4}E=1/16n4. The highly excited atoms are only detected in static fields less than 35 mV/cm, a field which roughly corresponds to field ionization of an atom bound by twice the microwave frequency. We also show that Na ∣m∣=1|m|=1∣m∣=1 atoms require a microwave field of E=1/9n4E=1/9{n}^{4}E=1/9n4 for ionization in zero static field, but the required field for ionization is reduced to E=1/3n5E=1/3{n}^{5}E=1/3n5 if a static field of 1 V/cm is present.
The 38-GHz microwave field required to effect 50% ionization of Li atoms decreases from 60 V/cm at n=37n=37n=37, where the microwave frequency is one-third the Kepler frequency, to 45 V/cm at n=56n=56n=56, where the microwave frequency is equal to the Kepler frequency. For n>56n>56n>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>215n>215n>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|m|=0 \mathrm{and} 1∣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 nnn and n+1n+1n+1 Stark manifolds of principal quantum numbers nnn and n+1n+1n+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|m|=2∣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=26n=26n=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.
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 1/16n4{\mathit{n}}^{4}n4 and 1/9n4{\mathit{n}}^{4}n4. At 670 MHz \ensuremath{\Vert}m\ensuremath{\Vert}=0, 1, and 2 states are all ionized at fields between 1/3n5{\mathit{n}}^{5}n5 and 1/9n4{\mathit{n}}^{4}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=1/3n5{\mathit{n}}^{5}n5, but the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states are unlikely to ionize at this field, with ionization occurring mostly at higher fields, 1/3n5{\mathit{n}}^{5}n5E1/9n4{\mathit{n}}^{4}n4, approaching the 15-GHz behavior of ionization at E=1/9n4{\mathit{n}}^{4}n4. At 4 GHz, Li n=20 \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states ionize at E=1/3n5{\mathit{n}}^{5}n5, but at n\ensuremath{\simeq}45, \ensuremath{\Vert}m\ensuremath{\Vert}=1 states ionize at E=1/9n4{\mathit{n}}^{4}n4, and the \ensuremath{\Vert}m\ensuremath{\Vert}=0 states ionize at E>1/3n5{\mathit{n}}^{5}n5. The \ensuremath{\Vert}m\ensuremath{\Vert}=2 states appear to ionize at E=1/9n4{\mathit{n}}^{4}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=1/9n4{\mathit{n}}^{4}n4 occurs at lower n. When a small static field is applied, the Li ionization threshold fields drop from 1/9n4{\mathit{n}}^{4}n4 to fields somewhat above 1/3n5{\mathit{n}}^{5}n5. Together the Na and Li measurements show that microwave ionization depends on a rate-limiting step, which is a resonant multiphoton transition.
Small static fields (\ensuremath{\cong}1 V/cm) are observed to reduce the microwave fields required to ionize highly excited $25\ensuremath{\le}n\ensuremath{\le}50$ Li atoms by about an order of magnitude, from \ensuremath{\cong}100 to 10 V/cm. This occurs because the static field splits series of multiply degenerate sideband states to form a quasicontinuum of closely spaced states, in which a sequence of resonant adsorptions occurs, allowing ionization at the lower microwave field.
We have measured the ionization fields for Na Rydberg states of $n\ensuremath{\ge}26$ by a 79-GHz microwave field. At low nnn, where the microwave frequency $\ensuremath{\omega}$ is one-third the classical Kepler frequency ${\ensuremath{\omega}}_{K}$, which is equal to the 1/n31/{n}^{3}1/n3 spacing between nnn states, the ionization field is $\ensuremath{\approx}1/3{n}^{5}$, in atomic units. As nnn is raised ${\ensuremath{\omega}}_{K}$ decreases, and the ionization field rises above 1/3n51/3{n}^{5}1/3n5, reaching a constant value when $\ensuremath{\omega}={\ensuremath{\omega}}_{K}$. At very high nnn, where $\ensuremath{\omega}>1/2{n}^{2}$, single photoionization is possible, and the measured rate agrees with the calculated value. These measurements, together with those done previously, connect the processes of field ionization and photoionization in Na. At low nnn and radio frequencies ionization is simply field ionization, and at very high nnn it occurs by photoionization, single-photon absorption. These measurements also show that microwave ionization of Rydberg atoms at 79 GHz results in significant populations' being left in the very high-lying states.