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Physical Review A

Ionization of sodium and lithium Rydberg atoms by 10-MHz to 15-GHz electric fields

Christopher R. Mahon, James L. Dexter, P. Pillet, Thomas F. Gallagher

Published Aug 1, 1991• 33 citations
Publisher

Abstract

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${\mathit{n}}^{4}$ and 1/9${\mathit{n}}^{4}$. At 670 MHz \ensuremath{\Vert}m\ensuremath{\Vert}=0, 1, and 2 states are all ionized at fields between 1/3${\mathit{n}}^{5}$ and 1/9${\mathit{n}}^{4}$, 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${\mathit{n}}^{5}$, 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${\mathit{n}}^{5}$E1/9${\mathit{n}}^{4}$, approaching the 15-GHz behavior of ionization at E=1/9${\mathit{n}}^{4}$. At 4 GHz, Li n=20 \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states ionize at E=1/3${\mathit{n}}^{5}$, but at n\ensuremath{\simeq}45, \ensuremath{\Vert}m\ensuremath{\Vert}=1 states ionize at E=1/9${\mathit{n}}^{4}$, and the \ensuremath{\Vert}m\ensuremath{\Vert}=0 states ionize at E>1/3${\mathit{n}}^{5}$. The \ensuremath{\Vert}m\ensuremath{\Vert}=2 states appear to ionize at E=1/9${\mathit{n}}^{4}$. 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${\mathit{n}}^{4}$ occurs at lower n. When a small static field is applied, the Li ionization threshold fields drop from 1/9${\mathit{n}}^{4}$ to fields somewhat above 1/3${\mathit{n}}^{5}$. Together the Na and Li measurements show that microwave ionization depends on a rate-limiting step, which is a resonant multiphoton transition.

DOI
10.1103/physreva.44.1859

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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.
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.
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.
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.
The ionization of Na atoms by 8-GHz electric fields from principal quantum number n=16--42 exhibits a threshold for the \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states of E\ensuremath{\approxeq}1/3n5{n}^{5}n5, and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9n4{n}^{4}n4 and E\ensuremath{\approxeq}1/21n4{n}^{4}n4 depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/n5{n}^{5}n5 scaling at high n which we interpret as being due to the fact that the relatively slower atomic frequencies at high n no longer match the 8 GHz microwave frequency. The E=1/21n4{n}^{4}n4 \ensuremath{\Vert}m\ensuremath{\Vert}=2 threshold has not to our knowledge been observed before, and we interpret it as arising from the ionization of the highest energy, or blue, Stark state at the classical limit for ionization.
Here we present experimental results connecting field ionization to photoionization in Li Rydberg atoms obtained with 17- and 36-GHz microwave fields. At a low principal quantum number nnn, where the microwave frequency $\ensuremath{\omega}$ is much lower than the classical, or Kepler frequency, ${\ensuremath{\omega}}_{K}=1/{n}^{3}$, microwave ionization occurs by field ionization, at E=1/9n4E=1/9{n}^{4}E=1/9n4. When the microwave frequency exceeds the Kepler frequency, $\ensuremath{\omega}>1/{n}^{3}$, the field required for ionization is independent of nnn and given by $E=2.4{\ensuremath{\omega}}^{5/3}$, in agreement with dynamic localization models, which cross over to a Fermi's Golden Rule approach at the photoionization limit. A surprising aspect of our results is that when $\ensuremath{\omega}\ensuremath{\approx}1/2{n}^{2}$, the one- and multiphoton ionization rates are similar, and even at the lowest microwave powers, all are 10 times lower than the perturbation theory rate calculated for single-photon ionization. Further, we show that when the Rydberg atoms are excited in the presence of the microwave field, the probability of an atom's being bound at the end of the microwave pulse passes smoothly across the limit. This microwave stimulated recombination to bound Rydberg states can be well described by a simple classical model. More generally, these results suggest that the problem of a Rydberg atom coupled to a high-frequency microwave field is similar to the problem of interchannel internal coupling in multilimit atoms, a problem well described by quantum defect theory.
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.