Physical Review A

Theory of resonant multiphoton ionization: Application to the cesium atom

Yves Gontier, M. Trahin

Published Jan 1, 1979• 97 citations

Abstract

A quantitative treatment is carried out for the exact operator expressions derived in a previous paper. The formalism of the dressed atom and the concept of level crossings (anticrossings) are used throughout and provide a basis for the quantitative investigation of the resonant three- and four-photon ionization of cesium. The numerical results obtained within this framework are in excellent agreement with experimental observations.

DOI: 10.1103/physreva.19.264

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Photoelectron angular distributions from multiphoton ionization of cesium atoms

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Physical Review AMay 1, 1974104 citations

Resonance shifts in the multiphoton ionization of cesium atoms

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Physical Review AJul 1, 1976107 citations

Physical Review A

Theory of resonant multiphoton ionization: Application to the cesium atom

Yves Gontier, M. Trahin

Published Jan 1, 1979• 97 citations

Publisher

Abstract

DOI: 10.1103/physreva.19.264

Related papers

Extended two-level model of multiphoton absorption

Joseph H. Eberly, Stephen V. O'Neil, Jacob L. F. de Meijere

Soviet Journal of Quantum ElectronicsOct 31, 19800 citations

Experimental multiphoton ionization of cesium atoms through the 9D 3/2 resonant level

G. Brincourt

Journal de Physique LettresJan 1, 19773 citations

Photoelectron angular distributions from multiphoton ionization of cesium atoms

R. N. Compton, John A. D. Stockdale, C. Dewey Cooper +2 more

We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p^{2}P_{\frac{1}{2},\frac{3}{2}}$ and $8p^{2}P_{\frac{1}{2},\frac{3}{2}}$ intermediate states and three-photon ionization via the two-photon-allowed $8d^{2}D_{\frac{5}{2},\frac{3}{2}}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the $^{2}P_{\frac{1}{2}}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the $^{2}P_{\frac{3}{2}}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the $^{2}P_{\frac{3}{2}}$ data.We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p^{2}P_{\frac{1}{2},\frac{3}{2}}$ and $8p^{2}P_{\frac{1}{2},\frac{3}{2}}$ intermediate states and three-photon ionization via the two-photon-allowed $8d^{2}D_{\frac{5}{2},\frac{3}{2}}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the $^{2}P_{\frac{1}{2}}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the $^{2}P_{\frac{3}{2}}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the $^{2}P_{\frac{3}{2}}$ data.

Physical Review AOct 1, 198437 citations

Near-infrared multiphoton ionization of cesium

William R. Christian, R. N. Compton, John A. D. Stockdale +4 more

Experimental and theoretical results are presented for resonantly enhanced three-photon ionization of cesium atoms in the wavelength range from 830 to 950 nm. The accidental near resonance of the $6p^{2}P_{\frac{3}{2},\frac{1}{2}}$ levels at the one-photon energy and the near resonance at the two-photon level with the $6d^{2}D_{\frac{3}{2},\frac{5}{2}}$ states gives rise to large ionization signals and interesting anomalies in the relative intensities of the fine-structure levels. "Hybrid resonances" are observed which involve the production of $6p ^{2}P_{\frac{1}{2}}$ atoms from molecular cesium. One hybrid resonance involves ionization of the $6p ^{2}P_{\frac{1}{2}}$ state via an electric quadrupole transition ($6p ^{2}P_{\frac{1}{2}}\ensuremath{-}7p ^{2}P_{\frac{3}{2}}$). Both experimental and theoretical photoelectron angular distributions are compared for all of the observed resonances except for the $6p ^{2}P_{\frac{3}{2}}$ state where the signals were too weak for such a measurement. Agreement between experiment and theory is fair for three-photon ionization via the $6p^{2}P_{\frac{1}{2}}$ state. Comparison of experiment and theory for the case of the $6d^{2}D_{\frac{3}{2},\frac{5}{2}}$ states indicates that hyperfine coupling during the laser-pulse duration may be important. The angular distributions for the hybrid resonances show the general behavior predicted by theory but the features appear broadened.Experimental and theoretical results are presented for resonantly enhanced three-photon ionization of cesium atoms in the wavelength range from 830 to 950 nm. The accidental near resonance of the $6p^{2}P_{\frac{3}{2},\frac{1}{2}}$ levels at the one-photon energy and the near resonance at the two-photon level with the $6d^{2}D_{\frac{3}{2},\frac{5}{2}}$ states gives rise to large ionization signals and interesting anomalies in the relative intensities of the fine-structure levels. "Hybrid resonances" are observed which involve the production of $6p ^{2}P_{\frac{1}{2}}$ atoms from molecular cesium. One hybrid resonance involves ionization of the $6p ^{2}P_{\frac{1}{2}}$ state via an electric quadrupole transition ($6p ^{2}P_{\frac{1}{2}}\ensuremath{-}7p ^{2}P_{\frac{3}{2}}$). Both experimental and theoretical photoelectron angular distributions are compared for all of the observed resonances except for the $6p ^{2}P_{\frac{3}{2}}$ state where the signals were too weak for such a measurement. Agreement between experiment and theory is fair for three-photon ionization via the $6p^{2}P_{\frac{1}{2}}$ state. Comparison of experiment and theory for the case of the $6d^{2}D_{\frac{3}{2},\frac{5}{2}}$ states indicates that hyperfine coupling during the laser-pulse duration may be important. The angular distributions for the hybrid resonances show the general behavior predicted by theory but the features appear broadened.

Physical Review AOct 1, 198411 citations

Theory of multiphoton ionization: Near-resonance effects in two-photon ionization

P. Lambropoulos

I present a perturbation theory of multiphoton ionization based on the resolvent operator. The theory is applied to a detailed study of two-photon ionization under near-resonance conditions. It is shown that a distinction must be made between linear level shifts and widths, and resonance shifts and widths which appear in the transition probability. The resonance shifts and widths exhibit saturation effects and their values tend to be much smaller than those of the linear level shifts and widths. Using numerical examples corresponding to tunable dye lasers and alkali-metal atoms, we show that the above shifts can have a dramatic effect on the ionization rate even when the laser is not in exact resonance with the intermediate level. The question of "one-step" vs "two-step" two-photon ionization is also discussed. It is shown that exact resonance does not necessarily imply a two-step process. In fact, in most cases it is quite the opposite. A quantitative criterion for this distinction is established. Finally, a distinction is made between instrumental saturation and saturation of the transition probability. The two are shown to be of different nature. Further extensions of the work are also discussed.I present a perturbation theory of multiphoton ionization based on the resolvent operator. The theory is applied to a detailed study of two-photon ionization under near-resonance conditions. It is shown that a distinction must be made between linear level shifts and widths, and resonance shifts and widths which appear in the transition probability. The resonance shifts and widths exhibit saturation effects and their values tend to be much smaller than those of the linear level shifts and widths. Using numerical examples corresponding to tunable dye lasers and alkali-metal atoms, we show that the above shifts can have a dramatic effect on the ionization rate even when the laser is not in exact resonance with the intermediate level. The question of "one-step" vs "two-step" two-photon ionization is also discussed. It is shown that exact resonance does not necessarily imply a two-step process. In fact, in most cases it is quite the opposite. A quantitative criterion for this distinction is established. Finally, a distinction is made between instrumental saturation and saturation of the transition probability. The two are shown to be of different nature. Further extensions of the work are also discussed.

Physical Review AMay 1, 1974104 citations

Resonance shifts in the multiphoton ionization of cesium atoms

J. Morellec, Didier Normand, G. Petite

This work reports the multiphoton ionization of cesium atoms, via resonance with the $6F$ level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\ensuremath{\rightarrow}6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction, ${K}_{\mathrm{expt}}$ . A sharp variation of ${K}_{\mathrm{expt}}$ is observed when the energy shift of the $6S\ensuremath{\rightarrow}6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\ensuremath{\rightarrow}6F$ transition is subject to theoretical reservations and needs further experimentation.This work reports the multiphoton ionization of cesium atoms, via resonance with the $6F$ level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\ensuremath{\rightarrow}6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction, ${K}_{\mathrm{expt}}$. A sharp variation of ${K}_{\mathrm{expt}}$ is observed when the energy shift of the $6S\ensuremath{\rightarrow}6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\ensuremath{\rightarrow}6F$ transition is subject to theoretical reservations and needs further experimentation.

Physical Review AJul 1, 1976107 citations

7p^{2}P_{\frac{1}{2},\frac{3}{2}}

and

8p^{2}P_{\frac{1}{2},\frac{3}{2}}

intermediate states and three-photon ionization via the two-photon-allowed

8d^{2}D_{\frac{5}{2},\frac{3}{2}}

resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the

^{2}P_{\frac{1}{2}}

states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the

^{2}P_{\frac{3}{2}}

resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the

^{2}P_{\frac{3}{2}}

data.

Experimental and theoretical results are presented for resonantly enhanced three-photon ionization of cesium atoms in the wavelength range from 830 to 950 nm. The accidental near resonance of the

6p^{2}P_{\frac{3}{2},\frac{1}{2}}

levels at the one-photon energy and the near resonance at the two-photon level with the

6d^{2}D_{\frac{3}{2},\frac{5}{2}}

states gives rise to large ionization signals and interesting anomalies in the relative intensities of the fine-structure levels. "Hybrid resonances" are observed which involve the production of

6p ^{2}P_{\frac{1}{2}}

atoms from molecular cesium. One hybrid resonance involves ionization of the

6p ^{2}P_{\frac{1}{2}}

state via an electric quadrupole transition ($6p ^{2}P_{\frac{1}{2}}\ensuremath{-}7p ^{2}P_{\frac{3}{2}}$). Both experimental and theoretical photoelectron angular distributions are compared for all of the observed resonances except for the

6p ^{2}P_{\frac{3}{2}}

state where the signals were too weak for such a measurement. Agreement between experiment and theory is fair for three-photon ionization via the

6p^{2}P_{\frac{1}{2}}

state. Comparison of experiment and theory for the case of the

6d^{2}D_{\frac{3}{2},\frac{5}{2}}

states indicates that hyperfine coupling during the laser-pulse duration may be important. The angular distributions for the hybrid resonances show the general behavior predicted by theory but the features appear broadened.

This work reports the multiphoton ionization of cesium atoms, via resonance with the

6F

level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\ensuremath{\rightarrow}6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction,

{K}_{\mathrm{expt}}

. A sharp variation of

{K}_{\mathrm{expt}}

is observed when the energy shift of the $6S\ensuremath{\rightarrow}6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\ensuremath{\rightarrow}6F$ transition is subject to theoretical reservations and needs further experimentation.