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Journal of Anhui Normal University

Theoretical Investigation on the(1+1′+1′) Resonant Ionization Dynamics of Three-level System

Zhifeng Cui

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The rate-equation and the Laplace transformation were used to study the three photons resonant ionization process of three-level system,and the analytical formulas of the resonant state populations and the ionization probabilities were obtained.By using this formulas to study the(1+1′+1′)resonant ionization process of Cs atom which are excited to the 6p(P_(3/2))、7d(D_(3/2)) resonant state from the ground state 6s(S_(1/2)) by the first two photons following the ionization by the third photon,the influence of the laser intensity and pulse width on the resonant state populations and ionization efficiency were investigated.The conditions of the laser intensity to evacuate the two resonant states population were also presented respectively.

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The rate-equation and the Laplace transformation were used to study the three photons resonant ionization process of three-level system,and the analytical formulas of the resonant state populations and the ionization probabilities were obtained.By using this formulas to study the(1+1′+1′)resonant ionization process of Cs atom which are excited to the 6p(P_(3/2))、7d(D_(3/2)) resonant state from the ground state 6s(S_(1/2)) by the first two photons following the ionization by the third photon,the influence of the laser intensity and pulse width on the resonant state populations and ionization efficiency were investigated.The conditions of the laser intensity to evacuate the two resonant states population were also presented respectively.
Based on the time-dependent density-matrix equations of two-level system,the analytical formule of the resonance-enhanced multiphoton ionization(REMPI) probabilities of atom were obtained under the resonant and near-resonant condition.Furthermore,for the(2+1) REMPI of oxygen atom with the 2p~34p as resonant state,the dependence of the ionization probability on laser intensity,pulse width and resonance detuning was discussed.At the same time,the relation of the saturation condition of REMPI to the laser intensity and the pulse width was derived.Under the near-resonant condition,the analytical results showed that the ionization probability decreased with the increase of resonance detuning with the fixed laser intensity and pulse width,and the ionization probability increased with the increase of laser intensity at the fixed resonance detuning and tended to become saturation when laser intensity was high enough.Under the resonant condition,the amplitude of the ionization probability increased rapidly with the pulse width when laser intensity increased.
Analytic expression of the ionization probability about 3+1 resonance enhanced multi-photon ionization (REMPI) process is deduced with the theory of rate equation, which implies the interaction of photon and material. Based on the expressions, the influence of laser intensity, laser pulse duration and spontaneous radiation lifetime on the ionization probability is analyzed theoretically. It is found that the ionization probability increases with laser intensity and laser pulse duration until gets to saturation. After that, the ionization probability will oscillate around the saturation value if laser intensity increases further. The amplitude of oscillation increases with laser intensity at first, and then it will decrease even get to zero after a maximum peak comes out. We attribute the appearance of the oscillation to the phenomena of quantum coherence caused by the splitting of energy level in strong laser field. As to the fact that the ionization probability becomes to zero with the increase of laser intensity, it indicates that laser intensity is strong enough so as to make the neutral particles getting to the region of ionization suppression. It is also found that the variation of ionization probability with spontaneous radiation lifetime is far smaller than the one with ionization rate. So the influence of the spontaneous radiation lifetime on ionization probability could be ignored.
The dynamical process of photoexcitation and photoionization of alkali atoms is studied with three-step laser pulses, focusing on the similarities and differences between Li and Cs atoms on their properties by making a comparison of them. Based on several excitation schemes, the present work not only establishes the rate equations of atom population for all related transition states, but also obtains the analytical solutions of photoexcitation and photoionization process. The mathematical solutions are simplified significantly by restricting the most general case to the several special cases, either designed or selected carefully, in order to highlight the main factors and obtain the physical insight underlying the complicated mathematical expressions. With self-programming, the possible impact of time configuration of laser pulses on the three-step laser excitation process of the photoexcitation and photoionization is calculated and studied systematically. Variation of the ionization efficiency with the laser parameters is investigated and discussed. With the same time configuration of laser pulses, the dependences of atom population for all the related transition states on the two different excitation paths are compared and analyzed, reflecting the impact of changing the atomic parameters. Under the similar excitation conditions, the differences of ionization efficiency between Li and Cs atoms are explored. Finally, based on the present study, several means for optimizing ionization efficiency are proposed.
This paper reports the four-photon ionization of caesium atoms when the laser frequency is tuned through the resonant three-photon transition 6S → 6F. This experiment was performed by using a tunable-wavelength bandwidth-limited subnanosecond laser pulse at 1.06 μm, in the 108-109 W.cm-2 laser intensity range. Pulse widths of 1.5 ns, 50 ps, and 15 ps were used. The resonant character of the multiphoton ionization process was observed, even with the shortest pulse of 15 ps. Nevertheless the influence of a temporal effect is demonstrated according to theoretical predictions. The resonance shift ΔE of the 6S → 6F transition energy was found to be linear with the laser intensity I within the range 108-109 W.cm-2. ΔE = α I, with α = 2 cm-1/GW.cm-2. This result confirms previous measurements performed with single-mode 35 ns laser pulses and is in very good agreement with calculated resonance shifts.
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.
In the present study we have investigated three-photon ionization in Ca in which autoionizing states are engaged. The two-photon resonant process (from the Ca ground state 4s 2 1 S 0 ) occurred through or at least in the vicinity of one of the following states: 4s4d 1 D 2 , 4p 2 3 P 2 , 4s6s 1 S 0 , 4p 2 1 D 2 and 4p 2 1 S 0 , with the third photon either reaching the continuum directly or one of the autoionizing states. The three-photon resonant transitions to 3d m p, m f: 1 P 1 , 3 P 1 and 3 D 1 autoionizing states for m up to 21 have been observed. Some of the autoionizing resonances which we have found had not been observed before in a high-resolution one-photon absorption experiment (for J = 1) and in multiphoton experiments (for J = 3). We have compared the ionization signal as a function of the laser detuning and the laser intensity with theoretical curves obtained within a simple model (three-level atom + one-mode laser field). This gives information about the order of magnitude of the three-photon ionization probability through autoionizing states.