Based on rate equation a theoretical study on laser power balance in a resonance multi-step ionization process of atoms has been presented in this paper.The calculation results made for a typical three-level atom show that there is an optimization laser power assignment when the total pumping laser power is limited,and under the optimization laser power assignment the ionization probability of a three-level atom can reach its maximum value.This conclusion is very different from that obtained under saturation excitation conditions.The method used here can be applied to more complicated multi-step ionization process of atoms.
Based on rate equation a theoretical study on laser power balance in a resonance multi-step ionization process of atoms has been presented in this paper.The calculation results made for a typical three-level atom show that there is an optimization laser power assignment when the total pumping laser power is limited,and under the optimization laser power assignment the ionization probability of a three-level atom can reach its maximum value.This conclusion is very different from that obtained under saturation excitation conditions.The method used here can be applied to more complicated multi-step ionization process of atoms.
Optimization of laser power balance is studied numerically for effective multi-step photoionization of degenerate atoms. To date, a large number of similar studies have been executed for simple nondegenerate atoms and, therefore, the emphasis in this study is placed on investigating the role of the level degeneracy. It is concluded that a monotonically increasing J-value in the excitation ladder of levels is preferable, which is followed by some variations thereof. It should also be noted that a reasonably high ionization rate is attainable, in any case, provided that the Rabi-frequencies are optimized at the expense of the sizable laser powers required. The computer code employed here, which deals with the population evolution among numerous magnetic sublevels, has been tested against experiments in advance of the above numerical study.
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.
Photoexcitation and photoionization of atoms, the central part of atom vapor laser isotope separation (AVLIS), relate to the ionization yield and isotope selectivity directly. Doppler broadening of absorption lines is one of the parameters that influence the photoexcitation and photoionization process of atoms. When evaporation temperature is high or beam equipment is absent, Doppler broadening has obvious influence on the ionization yield because most of atoms are non-resonantly excited. In this paper, we study the influences of Doppler broadening of absorption lines on a multi-step photoexcitation and photoionization process of atoms according to the facts of AVLIS. A Doppler-broadened three-level atom system with two resonant lasers is investigated. The interaction between laser field and atoms is described by a density matrix, which is calculated by fourth-order Runge-Kutta numerical method with variable steps. The results show that the ionization yield of atoms decreases with the increase of Doppler broadening of absorption lines under the same laser parameters. At a constant laser power, the ionization yield reaches its maximum value at the best laser bandwidths, which is different from that obtained without Doppler broadening, as reported in published papers. Meanwhile, the best laser bandwidth increases with the increase of Rabi frequency and Doppler broadening when other parameters are constant. Moreover, the best bandwidth of the second laser is smaller than that of the first laser in a multi-step photoionization process of atoms. Therefore, lasers should work at the best bandwidths in AVLIS for highest ionization yield. It is advantageous to make laser bandwidths slightly bigger than the best bandwidths technically for smaller fluctuation of ionization yield, owing to incoercible stochastic volatility in laser bandwidths. The ionization yield increases with the decrease of Doppler broadening, especially at the best laser bandwidths. Therefore, it is necessary to reduce Doppler broadening of atom vapor in laser ionization zone.
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.
A theoretical model of two-step resonant ionization which includes an autoionizing state is developed. The effects examined include interactions with a multimode laser and Zeeman and hyperfine multiplets. We approach this problem starting from first principles by treating the atom-radiation system as a unit. Theoretical analysis and numerical calculations of ionization probabilities are given. The intermode scattering is investigated in detail, and a simple physical interpretation of the dynamical effect is given. Comparisons of ionization probabilities for two-step processes with first-step excitations by single-mode or two-mode lasers are made. It is found that, if the mode spacing in a multimode-laser beam is less than the Doppler width of the atom, the multimode laser can more effectively produce ions than a single-mode laser does. This leads to the conclusion that the resonance effect is more important than the power-broadening effect. This is shown to be also true when Zeeman and hyperfine multiplets are included.
Atomic selective ionization processes provide critical ionization probability and isotopic selectivity in laser isotope separation. Aimed at the general principles of transition cross sections and ionization probabilities under various atomic hyperfine structures and laser parameters, and the optimization of atomic multi-channel photo-excitation and ionization processes of non-zero nuclear spin isotopes, the semi-classical density matrix theory of an imaginary two-step photoionization process is established with the consideration of magnetic sublevels of near-resonantly excited hyperfine levels. For determining the dimensionless transition cross sections of hyperfine transition channels, two methods are proposed in this article, i.e. the saturated excitation line-shape comparison method and weak excitation signal strength method, and a good agreement is achieved between numerical dimensionless transition cross sections and experimental results for several non-zero nuclear spin isotopes. The dependence of saturated ionization probability on laser polarization is studied systematically, and the hyperfine transition of Δ F = +1 is found to be superior to Δ F = −1, 0 in terms of saturated ionization probability. A general formula of oversaturated ionization probability is summarized for different hyperfine transitions. An interesting phenomenon called “magnetic sublevel coherence trapping” is employed to explain the inadequate ionization probability of the Δ F = −1 hyperfine transition even under the oversaturated excitation condition, and its mechanism is discussed through the temporal evolution of the density matrix elements. These numerical studies can provide beneficial references for laser isotope separation of isotopes with non-zero nuclear spin, as well as atomic laser spectroscopy.