In this paper, the dynamic characteristics of the two approaches of atomic ionization, photo-excitation plus photo-ionization (PE+PI) and the photo-excitation plus electric field ionization (PE+EFI) are investigated systematically. For the PE+PI process, two different schemes (I and II), with and without overlapping pulse duration, are designed and specified. The rate equations for both PE+PI and PE+EFI processes are established, numerical solutions of which provide profound characteristics. A detailed analysis of the theoretical results is carried out to observe the impacts on their overall ionization efficiency made by several factors, either atomic or laser parameters. Not only the ionization efficiency of both approaches is given, but also the optimal selection under some specific conditions is discussed. If the pulse widths of lasers are fixed, then the PE+EFI approach is superior to the PE+PI approach when laser powers are small, while the PE+PI approach is better otherwise.
In this paper, the dynamic characteristics of the two approaches of atomic ionization, photo-excitation plus photo-ionization (PE+PI) and the photo-excitation plus electric field ionization (PE+EFI) are investigated systematically. For the PE+PI process, two different schemes (I and II), with and without overlapping pulse duration, are designed and specified. The rate equations for both PE+PI and PE+EFI processes are established, numerical solutions of which provide profound characteristics. A detailed analysis of the theoretical results is carried out to observe the impacts on their overall ionization efficiency made by several factors, either atomic or laser parameters. Not only the ionization efficiency of both approaches is given, but also the optimal selection under some specific conditions is discussed. If the pulse widths of lasers are fixed, then the PE+EFI approach is superior to the PE+PI approach when laser powers are small, while the PE+PI approach is better otherwise.
The quantum statistical weight (G) of an atomic energy level is an important spectroscopic parameter, its effect on the atomic ionization process is, however, usually neglected for simplicity. In this work, the influences of the G parameters of the lithium atomic energy levels are taken into account explicitly for the first time in the study on the process of three-step photo-excitation (PE) + electric field ionization (EFI), which yields a significant effect on overall EFI efficiency of the PE+EFI process. With a set of specially designed PE+EFI schemes, the expected results are obtained. First, with a three-step PE scheme, the Li atom is excited by three pulsed lasers with different wavelengths, which are fired simultaneously, to one of the Rydberg states from its ground state, from which the Li atom is ionized by an electric-field pulse with a time delay in order to avoid the Stark effect. Based on the three physical processes the atom experiences the PE, none field, and the EFI processes, and a set of universal rate equations are established according to the conservation law of particle number with the knowledge of physical mechanism of the three different processes and the physical model set up for them, respectively. The G parameters of the four relevant bound energy states are displayed explicitly in the rate equations for the PE process to offer a clear viewabout their effect on the overall EFI efficiency of the PE+EFI process. Secondly, the overall efficiencies of PE+EFI process are calculated with the Matlab programming for the two specified excitation schemes, 2S1/22P1/23S1/225P1/2, 3/2 and 2S1/22P3/23D5/225F5/2, 7/2. The overall EFI efficiency of PE+EFI process is investigated not only by adjusting the laser parameters but also by comparing the results between the two different excitation schemes. In order to establish the relationship between the overall EFI efficiency and external field quantitatively, the dependence of population rate of the relevant bound states on various factors, such as laser and atomic parameters, is calculated systematically. The role of the G parameters of the relevant atomic energy levels played in the population rates is observed to determine which excitation scheme is better in terms of the population rate of the Rydberg state. Meanwhile, the spontaneous emission of the Rydberg state during the time delay between the pulses of electric field and laser is also evaluated to make a balance between avoiding the Stark effect and minimizing the spontaneous emission. Based on the analysis of the calculations, some new results are achieved. An enhancement of the overall EFI efficiency can be obtained by making a sophisticated design on the excitation scheme of the PE+EFI process to optimize the G parameters. The time delay between the pulses of electric field and laser not only lets the atom experience a field-free time period, but also makes an upper limit for the population rate of Rydberg state due to the redistribution of atom among the four relevant bound states in the period. The upper limit is found to be dependent on neither laser parameters nor the absolute values of the G parameters, while only on the branching ratio of the G parameters among those bound states. The overall EFI efficiency is dominated by the population rate of Rydberg state, as the EFI process may ionize all Rydberg atoms once the strength of the EFI field reaches the EFI threshold of the Rydberg state. Hence, the key factor for raising the overall EFI efficiency is to enhance the population rate of Rydberg state in the PE process, which is a hard challenge due to the upper limit for the population rate of Rydberg state.
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.
The atomic selective multi-step photoionization process is a critical step in laser isotope separation. In this work, we study three-step photoionization processes with non-monochromatic laser fields theoretically based on the semi-classical theory. Firstly, three bandwidth models, including the chaotic field model, de-correlation model, and phase diffusion model, are introduced into the density matrix equations. The numerical results are compared with each other comprehensively. The phase diffusion model is selected for further simulations in terms of the correspondence degree to physical practice. Subsequently, numerical calculations are carried out to identify the influences of systematic parameters, including laser parameters (Rabi frequency, bandwidth, relative time delay, frequency detuning) and atomic Doppler broadening, on photoionization processes. In order to determine the optimal match among different systematic parameters, the ionization yield of resonant isotope, and selectivity factor are adopted as evaluation indexes to guide the design and optimization process. The results in this work can provide a rewarding reference for laser isotope separation.
The selectivity of three-step pulse photo-ionization of atoms versus the detuning delta of exciting radiation frequencies from intermediate resonance is investigated in powerful laser fields where the power broadening of the resonant transitions is at least of the order of isotope shifts. The Doppler broadening of the resonant transitions is taken into account and it is assumed that the sum frequency of both exciting laser radiations is tuned to the line centre of the two-photon transition of a selected isotope. It is shown that in this situation the photo-ionization selectivity increases so greatly with the absolute detuning mod delta mod that even in such strong fields the process of photo-ionization can be highly selective. The optimization of selective photo-ionization of atoms is discussed in connection with the decrease in the selective isotope yield with increase of the absolute detuning mod delta mod . Analytical consideration of selective three-step pulse photo-ionization in powerful laser fields, based on the density matrix formalism, is presented together with the results of numerical simulation of the 40 Ca- 48 Ca laser isotope separation process as an example.
A theoretical analysis is made of the method of selective ionization of atoms based on selective resonance excitation by laser radiation to quantum states near the ionization threshold and subsequent autoionization decay of the excited states under the influence of an external electric field. The autoionization of atoms in static and pulsed electric fields is considered. Calculation formulas are obtained for the probability of autoionization of a hydrogenlike atom and corrections are computed for the influence of the electron shells. Numerical estimates are obtained for the autoionization of the n = 7–12 states of the Rb atom in an electric field.
Numerical computations of ionization efficiency and isotope selectivity of 176 L u have been carried out for the following three-step ladder type photoionization scheme, 5 d 6 s 2 2 D 3 / 2 ( 0.0 c m − 1 ) − − − ⟶ 540.4068 n m 5 d 6 s 6 p 4 F 5 / 2 o ( 18504.58 c m − 1 ) − − − ⟶ 535.0626 n m 5 d 6 s 7 s 4 D 3 / 2 ( 37193.98 c m − 1 ) − − − ⟶ 618.0061 n m 53375 c m − 1 A u t o i o n i z a t i o n S t a t e → L u + , by invoking the density matrix formalism for the laser–atom interactions. Equations of motion have been derived for the odd isotopes by inclusion of hyperfine levels. The line shapes and their effect on the ionization efficiency and isotope selectivity have been discussed in detail. The effects of power of excitation and ionization lasers, spectral bandwidths, pulse delays, Doppler broadening of the atomic ensemble on the ionization efficiency, and degree of enrichment have been presented. Optimum conditions for the power of excitation, detunings, and other system parameters for the selective yet efficient photoionization of 176 L u have been identified.