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Physical Review A

Resonant multiphoton ionization by finite-bandwidth chaotic fields

P. Zoller

Published Mar 1, 1979• 88 citations
Publisher

Abstract

Resonant multiphoton ionization by finite bandwidth multimode radiation is investigated without the restriction of either a "long" or a "short" correlation time of the field. By approximating the multimode radiation by a stochastic model of a chaotic field, the stochastic atomic-density-matrix equation is reduced to a tractable infinite set of differential equations. For a given bandwidth this set can be suitably truncated and numerically integrated. For large-bandwidth fields it turns out that these truncated equations constitute a systematic improvement of the method usually employed of decorrelating the atom-field variables. For zero-bandwidth fields the well-known result is recovered in that the statistical averaging of the ionization probability reduces to an average with respect to the Glauber $P$-distribution function of the chaotic field. Detailed results of numerical calculations for two-photon ionization are presented which reveal a number of new interesting features.

DOI
10.1103/physreva.19.1151

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Resonant multiphoton ionization by finite bandwidth multimode radiation is investigated without the restriction of either a "long" or a "short" correlation time of the field. By approximating the multimode radiation by a stochastic model of a chaotic field, the stochastic atomic-density-matrix equation is reduced to a tractable infinite set of differential equations. For a given bandwidth this set can be suitably truncated and numerically integrated. For large-bandwidth fields it turns out that these truncated equations constitute a systematic improvement of the method usually employed of decorrelating the atom-field variables. For zero-bandwidth fields the well-known result is recovered in that the statistical averaging of the ionization probability reduces to an average with respect to the Glauber PPP-distribution function of the chaotic field. Detailed results of numerical calculations for two-photon ionization are presented which reveal a number of new interesting features.
A Monte Carlo method has been successfully applied to the resonant multilevel photoionization by finite bandwidth lasers. A system of density matrix or Schrödinger equations is integrated numerically by using a time series of colored laser noises obeying the Langevin equation. Time dependence of the statistically averaged excitation probabilities is obtained by taking ensemble averages of trials with different stochastic initial conditions. It is found that the Monte Carlo results on the resonant two-level photoionization by a chaotic field model are in good agreement with those of Zollar. The results of the computer simulation show that this method is applicable to analyses of complex multilevel systems with statistical broadening such as the case in connection with the atomic laser isotope separation process. The numerical results using stochastic lasers by a modified version of the phase diffusion model, with spectrum falling off faster than a Lorentzian at its wings, are presented.
We consider the infinite-order set of coupled, integral equations for the states of an atom in a very-narrow-bandwidth classical radiation field. In the vicinity of a one-photon resonance for two-photon ionization, this set is reduced to a pair of coupled equations describing the response of the atom to the radiation field. This set is derived by dropping terms of the original set whose lowest-order contributions to the radiation-induced shift and width of the resonance are quadratic in the intensity. In the absence of simultaneous absorption and emission, impossible except for two-photon processes from excited states, this pair can be decoupled. The remaining uncoupled integral equation describes the ac Stark effect based on contributions to the shift and width linear in the intensity. These contributions derive from radiative corrections to the intermediate atomic state and depend on the virtual processes of ionization from and recombination into, as well as emission from and reabsorption into, this state. A method for obtaining the exact numerical solution is discussed. An approximate solution is obtained by use of the single-eigenfunction approximation to the Green's function belonging to the response function. This Green's function has a pole at the static (unshifted) position of the resonance; thus, this approximation is quite accurate very near the pole. The order of nonlinearity is calculated as a function of the static detuning through the resonance and is shown to undergo rapid fluctuations about the nonresonance value of 2. The error inherent in the single-eigenfunction approximation to the Green's function is estimated and found to range from about 1% to 27% corresponding to static detunings ranging from about 1 to 25 \AA{}, respectively.
Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.
Ionization characteristics of two-step excitation by two intense nonmonochromatic (finite bandwidth) lasers are investigated. By approximating the laser fields by a stochastic model of a chaotic field, the stochastic atomic-density-matrix equations for three-level atoms are first obtained. Comparing with the analytical solution, the accuracy of our model is confirmed. By using this model, the ionization characteristics are studied in detail as a function of laser bandwidth. The dependence of laser bandwidth on the Doppler averaged ionization probability is also investigated.
We derive a set of density matrix equations describing laser photo-excitation and ionization of atomic hydrogen in the presence of an external electric field. The equations are relevant as a description of multiphoton ionization of hydrogen (or deuterium) atoms in laser-produced transient plasmas. The laser wavelength is 243 nm, so that the photoionization is resonant with the 2 s 1/2 level. The electric field causes Stark mixing of the 2 s 1/2 level with the 2 p 1/2 and 2 p 3/2 levels. Because the electric field is taken in the same direction as the linear polarization of the laser, only states with equal m j are coupled, and the atom can be described with a four-level density matrix. The laser bandwidth is taken into account by using the stochastic model of a chaotic laser field introduced by Zoller [1]. We present a few calculations of the probabilities for ionization and excitation of a single hydrogen atom as a function of laser intensity and wavelength.
We present a detailed analysis of the effects of photon statistics on multiphoton ionization. Through a detailed study of the role of intermediate states, we evaluate the conditions under which the premise of nonresonant processes is valid. The limitations of its validity are manifested in the dependence of the process on the stochastic properties of the radiation and found to be quite sensitive to the intensity. The results are quantified through detailed calculations for coherent, chaotic, and squeezed vacuum radiation. Their significance in the context of recent developments in radiation sources such as the short-wavelength free-electron laser and squeezed vacuum radiation is also discussed.