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Physical Review A

Metastable states in microwave ionization

Alexandr Arakelyan, Thomas F. Gallagher

Published Feb 15, 2013• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.87.023410

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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≈2.4\ensuremathω5/3E\ensuremath{\approx}2.4{\ensuremath{\omega}}^{5/3}E\ensuremath≈2.4\ensuremathω5/3 until \ensuremath∼80\ensuremath{\sim}80\ensuremath∼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.
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.
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.
When atoms are exposed to intense laser or microwave pulses, $\ensuremath{\sim}10%$ of the atoms are found in Rydberg states subsequent to the pulse, even if it is far more intense than required for static field ionization. The optical spectra of the surviving Li atoms in the presence of a 38-GHz microwave field suggest how atoms survive an intense pulse. The spectra exhibit a periodic train of peaks 38 GHz apart. One peak is just below the limit, and with a 90-V/cm field amplitude the train extends from 300 GHz above the limit to 3000 GHz below it. The spectra and quantum-mechanical calculations imply that the atoms survive in quasistable states in which the Rydberg electron is in a weakly bound orbit infrequently returning to the ionic core during the intense pulse.
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 observed the microwave ionization of Na sss and ddd states with 8-GHz pulses as short as 600 ps full width at half maximum, i.e., pulses containing five cycles. We find the ionization probability to be strongly dependent on pulse length. For the shortest pulses, ionization probability of ∣m∣=0|m|=0∣m∣=0 and 1 states is approximately zero if a requirement for the minimum number of cycles is not met, even when the microwave amplitude exceeds the long-pulse threshold of E=1/3n5{E=1/3n}^{5}E=1/3n5. For the ∣m∣=2|m|=2∣m∣=2 states, which are approximately hydrogenic, essentially no ionization occurs with the shortest pulse until the microwave amplitude equals 1/9n4{1/9n}^{4}1/9n4. We also find that as many as 50% of the ∣m∣=0|m|=0∣m∣=0 and 1 atoms not ionized by the microwaves are left trapped in higher nnn levels than the one initially excited.
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.