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Chinese Journal of Lasers

Theoretical Investigation on the REMPI Processes of Two-Level System

Zhifeng Cui

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

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.

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Chinese Physics B•Oct 1, 2008•4 citations
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.
Photo-ionization probability is an important factor in the practical use of resonance enhanced multiphoton ionization (REMPI). To a certain experimental condition, it depends on the competition between spontaneous radiation and ionization of the excited particles. In this work, we investigate the influence of laser resonance detuning, Rabi frequency and ionization rate on spontaneous radiation and ionization in the process of REMPI with the theory of density matrix equation. A model of three energy level system is adopted. It is found that the spontaneous radiation and ionization probability increase with the decrease of laser resonance detuning. They get to the maximum when resonance detuning equals zero. The line width of spontaneous emission will decrease with the increase of ionization rate due to the competition between spontaneous radiation and ionization. In addition, the spontaneous radiation and ionization probability increase with Rabi frequency until gets to saturation. Laser resonance detuning has no influence on the saturation value. It only influences the Rabi frequency for saturation. If Rabi frequency increases further after saturation, the spontaneous radiation will decrease because of the phenomena of energy level splitting in strong laser field. Now that resonant absorption and large laser intensity can increase the ionization probability greatly, so we must select suitable laser frequency and large laser intensity in the practical use of REMPI, in order to get optimum detection result.
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.
In this paper we analyze two-photon-resonant three-photon ionization of atomic oxygen via the 2p3{\mathit{p}}^{3}p3(4{(}^{4}(4S\ifmmode^\circ\else\textdegree\fi{})np3{\mathit{np}}^{3}np3P0{\mathit{P}}_{0}P0​,1,2, and the 2p3{\mathit{p}}^{3}p3(4{(}^{4}(4S\ifmmode^\circ\else\textdegree\fi{})nf 3^{3}3F2{\mathit{F}}_{2}F2​,3,4 states. The various atomic parameters required for calculating the resonant enhanced multiphoton ionization (REMPI) probabilities are obtained using quantum-defect theory. The infinite sums over nonresonant states are truncated at a finite number of terms. Our calculated two-photon excitation cross sections agree well with the results of other recent calculations and of experimental measurements. The photoionization cross section is calculated for various electron kinetic energies. The REMPI dynamics is analyzed by solving the density-matrix equations. This framework consistently takes into account the effects of saturation and ac Stark shifts. REMPI probability is seen to be quite sensitive to the initial detuning, the intensity, and the particular resonant state accessed. The photoionization cross sections also imply that due to the rapid falloff of the cross section, two-color REMPI schemes with a lower-frequency ionizing photon would increase the effective REMPI probability.
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.
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.
This paper studies the multiphoton resonant ionization by two-colour laser pulses in the hydrogen atom by solving the time-dependent Schrodinger equation. By fixing the parameters of fundamental laser field and scanning the frequency of second laser field, it finds that the ionization probability shows several resonance peaks and is also much larger than the linear superposition of probabilities by applying two lasers separately. The enhancement of the ionization happens when the system is resonantly pumped to the excited states by absorbing two or more colour photons non-sequentially.