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Physical Review A

Two- and three-photon detachment of H− by a weak field

Daniel Proulx, Robin Shakeshaft

Published Sep 1, 1992• 36 citations
Publisher

Abstract

We describe a method for calculating rates for multiphoton detachment or ionization of a two-electron system by a perturbative field. We have applied the method to ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$, and we present estimates of two- and three-photon detachment rates. In particular, we explore the $^{1}$${\mathit{S}}^{\mathit{e}}$ and $^{1}$${\mathit{D}}^{\mathit{e}}$ Feshbach resonances below the n=2 and n=3 excitation thresholds of H; these resonances lie in the ``excess-photon detachment'' regime, where one photon is already sufficient to detach the electron.

DOI
10.1103/physreva.46.r2221

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Dynamic hyperpolarizability and two-photon detachment in the presence of a strong static electric field: Application to H^{-}

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Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of ${\mathrm{H}}^{\ensuremath{-}}$ in both laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order $(\ensuremath{\sim}{I}^{2})$ in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate $(S$-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner's threshold law for a short-range potential is discussed.

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Observation of resonant excess-photon detachment via a window resonance in the cesium negative ion

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Resonant two-color detachment of H− with excitation of H(n=2)

Ning-Yi Du, Anthony F. Starace, N. A. Cherepkov

The cross sections for resonant two-color, two-photon detachment of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ with excitation of the degenerate H(2s) and H(2p) levels are calculated within a semiempirical adiabatic hyperspherical representation. The first photon, with energy ${\mathrm{\ensuremath{\omega}}}_{1}$=0.4017 a.u., is resonant with the well-known Feshback $^{1}$${\mathit{P}}^{\mathit{o}}$ resonance below the H(n=2) threshold. The second photon, with energy ${\mathrm{\ensuremath{\omega}}}_{2}$\ensuremath{\ge}0.126 05 a.u., scans the energy region above the H(n=2) threshold over which long-range dipole-field-induced cross-section oscillations are predicted to occur. Such Gailitis-Damburg oscillations have not yet been observed experimentally. Results for various pairs of light polarization for the two photons are presented. Our resonant two-color, two-photon detachment cross sections are 8--9 orders of magnitude greater than the corresponding nonresonant, single-color, two-photon detachment cross sections obtained by Liu, Du, and Starace [Phys. Rev. A 43, 5891 (1991)]. Unmistakable evidence of long-range dipole-field effects is presented over the 5-meV energy range above the H(n=2) threshold. Furthermore, the differential cross sections for right- and left-circularly polarized, copropagating photons and especially the circular dichroism differential cross sections are shown to have nearly a full cycle of a greatly enhanced dipole-field-induced oscillation extending over the region from threshold to \ensuremath{\approxeq}34 meV above.

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Theory of multiphoton processes for atoms and ions

Bo Gao

In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.

•Jan 1, 1989•0 citations
We describe a method for calculating rates for multiphoton detachment or ionization of a two-electron system by a perturbative field. We have applied the method to H\ensuremath−{\mathrm{H}}^{\mathrm{\ensuremath{-}}}H\ensuremath−, and we present estimates of two- and three-photon detachment rates. In particular, we explore the ^{1}$${\mathit{S}}^{\mathit{e}} and ^{1}$${\mathit{D}}^{\mathit{e}} Feshbach resonances below the n=2 and n=3 excitation thresholds of H; these resonances lie in the ``excess-photon detachment'' regime, where one photon is already sufficient to detach the electron.
We report the measurement of the two-photon detachment spectrum of the 1De^{1}D^{e}1De resonance of ${\mathrm{H}}^{\ensuremath{-}}$ just below the n=2n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2n=2 threshold. The excess photon detachment resonance fits a Fano profile with energy 10.872(2) eV (relative to ${\mathrm{H}}^{\ensuremath{-}}$ ground state), a width of 0.0105(10) eV, and a shape parameter of $\ensuremath{-}8(2)$. To our knowledge, this describes the first time direct multiphoton excitation of a resonance has been observed in any negative atomic ion.
Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of ${\mathrm{H}}^{\ensuremath{-}}$ in both laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order $(\ensuremath{\sim}{I}^{2})$ in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate (S(S(S-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner's threshold law for a short-range potential is discussed.
Efficient excess-photon detachment to lowest nonvanishing order is observed with long (\ensuremath{\sim}0.7 ns) optical pulses and intensities of \ensuremath{\le}6\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 W/cm2{\mathrm{cm}}^{2}cm2. A Feshbach (``window'') resonance in ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$ suppresses single-photon detachment, while simultaneously enhancing the probability of absorption of one or more excess photons. The perspectives for future spectroscopic excess-photon detachment and studies of direct two-electron multiphoton detachment are briefly discussed.
The cross sections for resonant two-color, two-photon detachment of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ with excitation of the degenerate H(2s) and H(2p) levels are calculated within a semiempirical adiabatic hyperspherical representation. The first photon, with energy ${\mathrm{\ensuremath{\omega}}}_{1}$=0.4017 a.u., is resonant with the well-known Feshback 1^{1}1Po{\mathit{P}}^{\mathit{o}}Po resonance below the H(n=2) threshold. The second photon, with energy ${\mathrm{\ensuremath{\omega}}}_{2}$\ensuremath{\ge}0.126 05 a.u., scans the energy region above the H(n=2) threshold over which long-range dipole-field-induced cross-section oscillations are predicted to occur. Such Gailitis-Damburg oscillations have not yet been observed experimentally. Results for various pairs of light polarization for the two photons are presented. Our resonant two-color, two-photon detachment cross sections are 8--9 orders of magnitude greater than the corresponding nonresonant, single-color, two-photon detachment cross sections obtained by Liu, Du, and Starace [Phys. Rev. A 43, 5891 (1991)]. Unmistakable evidence of long-range dipole-field effects is presented over the 5-meV energy range above the H(n=2) threshold. Furthermore, the differential cross sections for right- and left-circularly polarized, copropagating photons and especially the circular dichroism differential cross sections are shown to have nearly a full cycle of a greatly enhanced dipole-field-induced oscillation extending over the region from threshold to \ensuremath{\approxeq}34 meV above.
In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.