Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Connecting field ionization to photoionization via 17- and 36-GHz microwave fields

J. H. Gurian, K. Richard Overstreet, H. Maeda, Thomas F. Gallagher

Published Oct 15, 2010• 11 citations
Publisher

Abstract

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 $n$, 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 $E=1/9{n}^{4}$. When the microwave frequency exceeds the Kepler frequency, $\ensuremath{\omega}>1/{n}^{3}$, the field required for ionization is independent of $n$ 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.

DOI
10.1103/physreva.82.043415

Related papers

Ionization of Na Rydberg atoms by a 79-GHz microwave field

Alexandr Arakelyan, Jirakan Nunkaew, Thomas F. Gallagher

We have measured the ionization fields for Na Rydberg states of $n\ensuremath{\ge}26$ by a 79-GHz microwave field. At low $n$, where the microwave frequency $\ensuremath{\omega}$ is one-third the classical Kepler frequency ${\ensuremath{\omega}}_{K}$, which is equal to the $1/{n}^{3}$ spacing between $n$ states, the ionization field is $\ensuremath{\approx}1/3{n}^{5}$, in atomic units. As $n$ is raised ${\ensuremath{\omega}}_{K}$ decreases, and the ionization field rises above $1/3{n}^{5}$, reaching a constant value when $\ensuremath{\omega}={\ensuremath{\omega}}_{K}$. At very high $n$, 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 $n$ and radio frequencies ionization is simply field ionization, and at very high $n$ 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.

Physical Review A•Nov 17, 2016•19 citations

Microwave ionization of Na Rydberg atoms

P. Pillet, H. B. van Linden van den Heuvell, W. W. Smith +3 more

Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The $|m|=0 \mathrm{and} 1$ 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.

Physical Review A•Jul 1, 1984•81 citations

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

Christopher R. Mahon, James L. Dexter, P. Pillet +1 more

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.

Physical Review A•Aug 1, 1991•33 citations

IONIZATION OF RYDBERG ATOMS BY CIRCULARLY POLARIZED MICROWAVE FIELDS

Thomas F. Gallagher

In circularly polarized microwave fields of frequencies in the vicinity of 10 GHz ionization of Na Rydberg atoms occurs at a field E=1/16n4, up to principal quantum number n=50. This field is equal to the classical field for ionization and the static field required to ionize a Na atom. On the other hand, this field is far below the linearly polarized 10 GHz field required to ionize Na atoms, E=1/3n5. If the problem is transformed to a frame rotating with the microwave field, the field becomes a static field. In this case it is straightforward to calculate the ionization field classically. However, it is far lower than the experimentally observed field, a discrepancy which may be due to an angular momentum barrier.

Modern Physics Letters B•Feb 20, 1991•18 citations

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

Alexandr Arakelyan, Thomas F. Gallagher

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.

Physical Review A•May 14, 2014•1 citation

Metastable states in microwave ionization

Alexandr Arakelyan, Thomas F. Gallagher

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.

Physical Review A•Feb 15, 2013•8 citations
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 \ensuremathω\ensuremath{\omega}\ensuremathω is much lower than the classical, or Kepler frequency, \ensuremathωK=1/n3{\ensuremath{\omega}}_{K}=1/{n}^{3}\ensuremathωK​=1/n3, 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, \ensuremathω>1/n3\ensuremath{\omega}>1/{n}^{3}\ensuremathω>1/n3, the field required for ionization is independent of nnn and given by E=2.4\ensuremathω5/3E=2.4{\ensuremath{\omega}}^{5/3}E=2.4\ensuremathω5/3, 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 \ensuremathω\ensuremath≈1/2n2\ensuremath{\omega}\ensuremath{\approx}1/2{n}^{2}\ensuremathω\ensuremath≈1/2n2, 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.
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.
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 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.
In circularly polarized microwave fields of frequencies in the vicinity of 10 GHz ionization of Na Rydberg atoms occurs at a field E=1/16n4, up to principal quantum number n=50. This field is equal to the classical field for ionization and the static field required to ionize a Na atom. On the other hand, this field is far below the linearly polarized 10 GHz field required to ionize Na atoms, E=1/3n5. If the problem is transformed to a frame rotating with the microwave field, the field becomes a static field. In this case it is straightforward to calculate the ionization field classically. However, it is far lower than the experimentally observed field, a discrepancy which may be due to an angular momentum barrier.
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.