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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Dynamic shift in single-color two-step three-photon ionization

Yongjoo Rhee, A. S. Choe, Jongmin Lee, Marina A. Kuzmina, В. А. Мишин

Published May 6, 1996• 0 citations
Publisher

Abstract

A single-color, two-step, three-photon ionization is examined in a point of view of the dynamic shift of two-photon resonance within the framework of the Bloch equation. It is suggested that a formula well-describes the dynamic shift even beyond usual quadratic behavior and it corresponds to the laser-frequency detuning causing a complete population transfer to the third-bound level.

DOI
10.1117/12.239729

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A single-color, two-step, three-photon ionization is examined in a point of view of the dynamic shift of two-photon resonance within the framework of the Bloch equation. It is suggested that a formula well-describes the dynamic shift even beyond usual quadratic behavior and it corresponds to the laser-frequency detuning causing a complete population transfer to the third-bound level.
The 4-photon 3-step ionization scheme was analyzed by using Bloch equations. The effect of laser bandwidth was considered in accordance with the decorrelation method. For monochromatic lasers, the coherent population trapping was observed and the effects of detunings and Rabi frequencies on the ionization characteristics were studied. For nonmonochromatic lasers, the coherent population trapping was not observed and the enhancement of ionization at large detunings was observed. In order to evaluate the selectivity, the ionization probability of atoms which have detuning of 5 GHz for each excitation step was examined. Two small ionization peaks were observed for nonmonochromatic lasers while only peak was observed for monochromatic lasers. However sufficiently high selectivity can be expected over detunings.
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.
Within the framework of a three-level model, the process of three-photon ionization with one-photon resonance between two excited levels (with the lower one being initially unpopulated) is considered using the density matrix method. It is shown that such resonance can result in the appearance of a maximum in the three-photon ionization spectrum when detuning between the resonance wavenumber and the wavenumber of the transition responsible for the lower excited level being populated exceeds the laser radiation linewidth by more than three orders of magnitude.
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.
We examine the excitation dynamics of a model atom excited by a two-colour laser field. Here the two colours or frequencies are the fundamental and its third harmonic. The atomic model consists of two bound states which are near-resonantly coupled by a three-photon excitation by the fundamental and a one-photon excitation by the third harmonic, and a structureless continuum. We investigate how the laser parameters (intensity and frequency) and the relative phase between the two colours affects the degree of phase modulation in the ionization signal. We compare our findings from this simple model atom with those from more realistic atomic models by carrying out numerical integration of the hydrogenic Schrodinger equation in both one and three dimensions.