Physical Review A

Above-threshold ionization at 8 GHz

Thomas F. Gallagher, T. J. Scholz

Published Sep 1, 1989• 14 citations

Abstract

We report measurements of the energies of electrons ejected from Rydberg atoms by strong microwave fields. For high-n Rydberg states we observe double-peaked electron-energy spectra, with peaks at both one and three times the ponderomotive energy. The observation of both peaks confirms the validity of the classical picture used to describe above-threshold ionization at low frequencies.

DOI: 10.1103/physreva.40.2762

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

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Phase-sensitive above-threshold ionization of Rydberg atoms at 8 GHz

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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

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Microwave ionization of Na Rydberg atoms

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Physical Review A

Above-threshold ionization at 8 GHz

Thomas F. Gallagher, T. J. Scholz

Published Sep 1, 1989• 14 citations

Publisher

Abstract

DOI: 10.1103/physreva.40.2762

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.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 ANov 17, 201619 citations

Phase-sensitive above-threshold ionization of Rydberg atoms at 8 GHz

Duncan Tate, Dimitrios G. Papaioannou, Thomas F. Gallagher

We have observed the phase dependence of microwave above-threshold ionization (ATI) of Rydberg potassium atoms at a microwave intensity of 3\ifmmode\times\else\texttimes\fi{} ${10}^{4}$ W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. By using 5-ps pulses derived from a mode-locked tunable dye laser to create the initial Rydberg state, and phase locking the microwave field to a high harmonic of the mode-locking frequency, we are able to excite the atom at a specific phase of the microwave field. Measurement of the ejected electrons' energy as a function of the initial Rydberg state and the phase of the microwave field show that it is the phase of the field at which the electron becomes free of the atom that determines its kinetic energy. The energy dependence is described by a simple, classical theory that reveals the relationship between the so-called ``quiver'' and ``drift'' terms in the electron energy previously observed in ATI experiments at higher frequencies.We have observed the phase dependence of microwave above-threshold ionization (ATI) of Rydberg potassium atoms at a microwave intensity of 3\ifmmode\times\else\texttimes\fi{}${10}^{4}$ W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. By using 5-ps pulses derived from a mode-locked tunable dye laser to create the initial Rydberg state, and phase locking the microwave field to a high harmonic of the mode-locking frequency, we are able to excite the atom at a specific phase of the microwave field. Measurement of the ejected electrons' energy as a function of the initial Rydberg state and the phase of the microwave field show that it is the phase of the field at which the electron becomes free of the atom that determines its kinetic energy. The energy dependence is described by a simple, classical theory that reveals the relationship between the so-called ``quiver'' and ``drift'' terms in the electron energy previously observed in ATI experiments at higher frequencies.

Physical Review ANov 1, 199013 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.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 AAug 1, 199133 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

Spectrum of quasistable states in a strong microwave field

Alexandr Arakelyan, Türker Topçu, F. Robicheaux +1 more

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.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.

arXiv:1404.5602Physical Review AJul 14, 20147 citations

Ionization of Na atoms by 8-GHz electric fields

H. B. van Linden van den Heuvell, Thomas F. Gallagher

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}1/3 ${n}^{5}$ , and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9 ${n}^{4}$ and E\ensuremath{\approxeq}1/21 ${n}^{4}$ depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/ ${n}^{5}$ 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=1/21 ${n}^{4}$ \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.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}1/3${n}^{5}$, and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9${n}^{4}$ and E\ensuremath{\approxeq}1/21${n}^{4}$ depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/${n}^{5}$ 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=1/21${n}^{4}$ \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.

Physical Review ASep 1, 198520 citations

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.

We have observed the phase dependence of microwave above-threshold ionization (ATI) of Rydberg potassium atoms at a microwave intensity of 3\ifmmode\times\else\texttimes\fi{}

{10}^{4}

W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. By using 5-ps pulses derived from a mode-locked tunable dye laser to create the initial Rydberg state, and phase locking the microwave field to a high harmonic of the mode-locking frequency, we are able to excite the atom at a specific phase of the microwave field. Measurement of the ejected electrons' energy as a function of the initial Rydberg state and the phase of the microwave field show that it is the phase of the field at which the electron becomes free of the atom that determines its kinetic energy. The energy dependence is described by a simple, classical theory that reveals the relationship between the so-called ``quiver'' and ``drift'' terms in the electron energy previously observed in ATI experiments at higher frequencies.

{\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.

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.

{n}^{5}

, and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9

{n}^{4}

and E\ensuremath{\approxeq}1/21

{n}^{4}

depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/

{n}^{5}

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=1/21

{n}^{4}

\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.