The four-color three-step selective photoionization process of atom is very important in laser isotope separation technology. The population trapping phenomena and their influences are studied theoretically in monochromatic and non-monochromatic laser fields based on the density matrix theory in this work. Time evolutions of the photoionization properties of the four-color, three-step process are given. The population trapping effects occur intensely in monochromatic excitation, while it gradually turns weak as the laser bandwidth increases. The effects of bandwidth, Rabi frequency, time delay, and frequency detuning on the population trapping effect are investigated in monochromatic and non-monochromatic laser fields. The effects of laser process parameters and atomic parameters on the effective selective photoionization are also discussed. The ionization probability and selectivity factors, as evaluation indexes, are difficult to improve synchronously by adjusting systematic parameters. Besides, the existence of metastable state may play a negative role when its population is low enough.
The four-color three-step selective photoionization process of atom is very important in laser isotope separation technology. The population trapping phenomena and their influences are studied theoretically in monochromatic and non-monochromatic laser fields based on the density matrix theory in this work. Time evolutions of the photoionization properties of the four-color, three-step process are given. The population trapping effects occur intensely in monochromatic excitation, while it gradually turns weak as the laser bandwidth increases. The effects of bandwidth, Rabi frequency, time delay, and frequency detuning on the population trapping effect are investigated in monochromatic and non-monochromatic laser fields. The effects of laser process parameters and atomic parameters on the effective selective photoionization are also discussed. The ionization probability and selectivity factors, as evaluation indexes, are difficult to improve synchronously by adjusting systematic parameters. Besides, the existence of metastable state may play a negative role when its population is low enough.
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 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.
The population inversion in a three-level atomic system, interacting with two coherent laser pulses, occurs from the first level to the third level at the optimal detunings of the laser frequencies near the two-photon resonance. An examination is performed to see whether the energy density and time-delay of the photoionizing laser can significantly influence the ion yield for the case where the atom interacts with two coherent pulses and one photoionizing pulse incoherently coupled. The well-known three-colour, three-step, three-photon ionization scheme, which is available for the selective photoionization of 168Yb, is chosen for use in this research with the Bloch equation. It is revealed that the proper time-delay and energy density enable us to achieve higher efficiency for the selective photoionization of 168Yb, regardless of the Doppler-broadening, though the efficiency and selectivity of coherent excitation are prominently enhanced by applying the optimal detunings.
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.
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.
Abstract The laser frequency spectrum, whose full width at half-maximum in the frequency domain is the laser bandwidth, plays a critical role in atomic multi-step photoionization processes and has a significant influence on isotopic selective photoionization results. In this study, two phase-independent frequency spectrum models, that is, the mode jitter model (MJ model) based on the mode jitter phenomenon and the multi-longitudinal mode model (MLM model) based on multi-longitudinal mode output, are proposed to describe the spectral characteristics in the frequency domain. In the MJ model, it is assumed that there is a time-varying longitudinal mode in each laser pulse, with different central frequencies between adjacent pulses in the pulse train; in the MLM model, it is assumed that multiple longitudinal modes are output simultaneously with fixed central frequencies. Selective photoionization properties of these two frequency spectrum models and the chaotic field model are simulated and compared with each other under the Lorentzian frequency spectrum condition. Influences of the excitation intensity, laser frequency spectral profile and cutoff frequency on selective photoionization processes are calculated and compared among the above-mentioned three frequency spectrum models. Finally, the measurement of the laser frequency spectrum and the introduction of individual longitudinal modes’ bandwidths are discussed.