Physical Review A

Microwave multiphoton ionization and excitation of helium Rydberg atoms

Willem van de Water, Suzanne Yoakum, Ton van Leeuwen, B. E. Sauer, Leo Moorman, Enrique J. Galvez, David R. Mariani, Peter M. Koch

Published Jul 1, 1990• 40 citations

Publisher

Abstract

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_{0}$ $^{3}$S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_{0}$=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_{0}$ $^{3}$S\ensuremath{\rightarrow}${\mathit{n}}_{0}$ $^{3}$L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

DOI: 10.1103/physreva.42.572

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Microwave multiphoton excitation of helium Rydberg atoms: The analogy with atomic collisions

Willem van de Water, K. A. H. van Leeuwen, Suzanne Yoakum +5 more

Physical Review LettersAug 14, 198914 citations

Ionization and excitation of hydrogen and helium Rydberg atoms by microwaves

Leo Moorman, B. E. Sauer, Suzanne Yoakum +4 more

AIP conference proceedingsJan 1, 19901 citation

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

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Physical Review AOct 15, 201011 citations

Rydberg atoms ionization by microwave field and electromagnetic pulses

B. Kaulakys, G. Vilutis

AIP conference proceedingsJan 1, 19951 citation

Microwave ionization of Rb Rydberg atoms: Frequency dependence

Leszek Sirko, Markus Arndt, P. M. Koch +1 more

Physical Review AMay 1, 19947 citations

Microwave ionization of Na Rydberg atoms

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

Physical Review AJul 1, 198481 citations

Physical Review A

Microwave multiphoton ionization and excitation of helium Rydberg atoms

Willem van de Water, Suzanne Yoakum, Ton van Leeuwen, B. E. Sauer, Leo Moorman, Enrique J. Galvez, David R. Mariani, Peter M. Koch

Published Jul 1, 1990• 40 citations

Publisher

Abstract

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited

{\mathit{n}}_{0}

^{3}

S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range

{\mathit{n}}_{0}

=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of

{\mathit{n}}_{0}

^{3}

S\ensuremath{\rightarrow}

{\mathit{n}}_{0}

^{3}

L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

DOI: 10.1103/physreva.42.572

Related papers

Microwave multiphoton excitation of helium Rydberg atoms: The analogy with atomic collisions

Willem van de Water, K. A. H. van Leeuwen, Suzanne Yoakum +5 more

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the ${n}^{3}$ S to ${n}^{3}$ (L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the ${n}^{3}$S to ${n}^{3}$(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

Physical Review LettersAug 14, 198914 citations

Ionization and excitation of hydrogen and helium Rydberg atoms by microwaves

Leo Moorman, B. E. Sauer, Suzanne Yoakum +4 more

We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.

AIP conference proceedingsJan 1, 19901 citation

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

J. H. Gurian, K. Richard Overstreet, H. Maeda +1 more

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.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.

Physical Review AOct 15, 201011 citations

Rydberg atoms ionization by microwave field and electromagnetic pulses

B. Kaulakys, G. Vilutis

A simple theory of the Rydberg atoms ionization by electromagnetic pulses and microwave field is presented. The analysis is based on the scale transformation which reduces the number of parameters and reveals the functional dependencies of the processes. It is shown that the observed ionization of Rydberg atoms by subpicosecond electromagnetic pulses scale classically. The threshold electric field required to ionise a Rydberg state may be simply evaluated in the photonic basis approach for the quantum dynamics or from the multiphoton ionization theory.A simple theory of the Rydberg atoms ionization by electromagnetic pulses and microwave field is presented. The analysis is based on the scale transformation which reduces the number of parameters and reveals the functional dependencies of the processes. It is shown that the observed ionization of Rydberg atoms by subpicosecond electromagnetic pulses scale classically. The threshold electric field required to ionise a Rydberg state may be simply evaluated in the photonic basis approach for the quantum dynamics or from the multiphoton ionization theory.

AIP conference proceedingsJan 1, 19951 citation

Microwave ionization of Rb Rydberg atoms: Frequency dependence

Leszek Sirko, Markus Arndt, P. M. Koch +1 more

We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np ${)}^{2}$ ${\mathit{P}}_{3/2}$ (\ensuremath{\Vert} ${\mathit{M}}_{\mathit{J}}$ \ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np${)}^{2}$${\mathit{P}}_{3/2}$(\ensuremath{\Vert}${\mathit{M}}_{\mathit{J}}$\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.

Physical Review AMay 1, 19947 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.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 AJul 1, 198481 citations

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited

{\mathit{n}}_{0}

^{3}

S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range

{\mathit{n}}_{0}

{\mathit{n}}_{0}

^{3}

S\ensuremath{\rightarrow}

{\mathit{n}}_{0}

^{3}

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the

{n}^{3}

S to

{n}^{3}

(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

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.

We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np

{)}^{2}

{\mathit{P}}_{3/2}

(\ensuremath{\Vert}

{\mathit{M}}_{\mathit{J}}

\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.

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.