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Journal of the Physical Society of Japan

Theory of Two-Photon Excitation and Three-Photon Ionization of Atom by Laser Light

Toshihiko Ohno, Takayoshi Okuda

Published Aug 1, 1976• 4 citations
Publisher

Abstract

The probability of two-photon excitation of an atom by the intense laser light is calculated formally and the probability per unit time of the three-photon ionization of an atom by the laser light with finite spectral line width is obtained for the case where a two-photon resonance occurs in an intermediate atomic level and the line shape of the laser light is Lorentzian. It is shown that the probability of three-photon ionization is proportional to the square of photon flux in the case of low photon flux and large spectral line width.

DOI
10.1143/jpsj.41.590

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Canadian Journal of Physics•Dec 1, 1981•16 citations
The probability of two-photon excitation of an atom by the intense laser light is calculated formally and the probability per unit time of the three-photon ionization of an atom by the laser light with finite spectral line width is obtained for the case where a two-photon resonance occurs in an intermediate atomic level and the line shape of the laser light is Lorentzian. It is shown that the probability of three-photon ionization is proportional to the square of photon flux in the case of low photon flux and large spectral line width.
At three-photon barium and strontium atom ionization the intermediate two-photon resonances with the triplet states were discovered. The ion yield maxima corresponding to two-photon singlet-singlet and singlet-triplet resonances have approximately the same amplitude. Large probability of two-photon excitation of the triplet states sharply differed from the case for one-photon excitation. The possible reasons leading to large probabilities of two-photon excitation of the triplet states are discussed.
The manifestation of double resonances upon the three-photon ionization of the samarium atom has been studied in a frequency range of 17200–18400 cm −1 . Thirty peaks caused by double resonances have been found in the dependence of the yield of Sm + ions on the laser radiation frequency. The majority of these peaks greatly exceed in amplitude the peaks associated with ordinary two-photon resonances. The influence of double resonances on the three-photon ionization has been theoretically analyzed using the density matrix approximation. The calculations show that the probability of the three-photon resonance ionization can increase by more than two orders of magnitude due to the additional one-photon population of an intermediate level. The double resonance slows down the rate of increase in the probability of ionization with an increase in the laser radiation intensity compared to ordinary two-photon resonance.
Orer a small range of light intensity the three-photon ionization rate of caesium atoms by ruby laser light decreases when the incident photon flux is increased. This result may be quantitatively explained by an induced energy shift of the 913 levels of the caesium atom proportional to the square of the light intensity. Thus perturbations of bound electron states by an intense light beam can be of importance in determining the multiphoton ionization rate. In this paper the functional dependence of the ionization rate on the photon flux is calculated for caesium, using a perturbation theory somewhat different from that usually employed.
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.
A two-state atom in a perturber gas is irradiated by intense light with an arbitrary spectral profile. The authors derive a general expression for the fluorescence spectrum in terms of the conventional low-intensity absorption profile and the spectral density of the incident light. This result, which contains previous results as special limiting cases, describes the transition from the three-line fluorescence spectrum excited by intense monochromatic light and the power-broadened Lorentzian spectrum produced by broad-band excitation.
We have studied the excitation spectrum arising from the optical mixing of the frequencies of a strong bichromatic field interacting with a three-level atom, where the two initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. In the limit of high photon densities, the excitation spectrum near the frequency ω = ωa – 2ωb has been calculated as a function of the parameter η = Ωa2/Ωb2, where Ωa and Ωb are the Rabi frequencies of the two laser fields, respectively. For [Formula: see text] and for weak fields for which [Formula: see text], the spectral function describes a Lorentzian line peaked at the frequency ω = ωa – 2ωb and has a width of the order of γ0, where γ0/2 is the natural width for a two-level atom. When Ωb2 > γ02 and [Formula: see text], the band at ω = ωa – 2ωb splits into two bands described by two Lorentzian lines peaked at ω = ωa – 2ωb ± Ωb/√2 and have spectral widths of the order of 3γ0/4. The ratio of the height of the band ω = ωa – 2ωb to the height ω = ωa – 2ωb ± Ωb/2 is 3:2. The probability amplitudes for both bands take large negative values indicating that optical amplification of the signal field may be expected to occur at these frequencies. When Ωa = Ωb = Ω, η = 1, and for Ω2 < γ02, the spectral function describes a single band at ω = ωa – 2ωb while for Ω2 > γ02, the single band splits into five pairs of bands which are separated from the frequency ω = ωa – 2ωb by frequency shifts which are equal to: ± Ω/√2, [Formula: see text], ± Ω, ± Ω√2, and ± Ω√3, respectively, and have spectral widths of the order of 3γ0/4. For [Formula: see text] and for laser fields for which Ωa2 > γ02 and Ωb2 > γ02, the spectral function consists of three pairs of bands. The probability amplitudes for these bands vary linearly with η and may take large values for [Formula: see text]. A complete discussion of the excitation spectrum as well as a graphical representation of the derived results has been given.