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Numerical simulation of the photon absorption cross-section of 87Rb D1 line

Zhichao Ding, Jiajia Li, Jie Yuan

Published Oct 24, 2017• 1 citation
Publisher

Abstract

For realizing optimal performance, knowing the photon absorption cross-section of alkali atoms is significant in a wide range of fields, such as atomic clock, atomic magnetometer and atomic spin gyroscope. By analyzing the pressure broadening and shift, natural broadening and Doppler broadening of the absorption line of 87Rb D1 line, the numerical simulation of photon absorption cross-section of 87Rb D1 line is conducted. Based on the results of numerical simulation, natural broadening is found to be much smaller than pressure broadening and Doppler broadening in general. The pressure broadening becomes the dominant factor of broadening for high pressure of buffer and quenching gases, while the Doppler broadening is dominant for low pressure of buffer and quenching gases. The results of numerical simulation demonstrate that, with the increasing broadening of absorption line, the number of peaks of the photon absorption cross-section decreases from four to one gradually, and the amplitudes of these peaks decline in the meantime.

DOI
10.1117/12.2282551

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For realizing optimal performance, knowing the photon absorption cross-section of alkali atoms is significant in a wide range of fields, such as atomic clock, atomic magnetometer and atomic spin gyroscope. By analyzing the pressure broadening and shift, natural broadening and Doppler broadening of the absorption line of 87Rb D1 line, the numerical simulation of photon absorption cross-section of 87Rb D1 line is conducted. Based on the results of numerical simulation, natural broadening is found to be much smaller than pressure broadening and Doppler broadening in general. The pressure broadening becomes the dominant factor of broadening for high pressure of buffer and quenching gases, while the Doppler broadening is dominant for low pressure of buffer and quenching gases. The results of numerical simulation demonstrate that, with the increasing broadening of absorption line, the number of peaks of the photon absorption cross-section decreases from four to one gradually, and the amplitudes of these peaks decline in the meantime.
Reliable modeling of pressure-broadened spectra is essential for maintaining physical consistency in alkali vapor-cell diagnostics. In this work, we investigate the low-power absorption spectra of isotopically enriched 87Rb vapor cells at the D1 and D2 transitions, systematically comparing three fitting algorithms: single Lorentzian, hyperfine-resolved Voigt, and the doublet Lorentzian approximation. Experiments were performed across optical intensities from 40 nW to 10 mW, buffer-gas pressures from 200 Torr to 520 Torr, and temperatures between 370 K and 390 K. It is shown that when the pressure broadening dominates over Doppler broadening and the optical intensity remains below the saturation regime, the reduced doublet Lorentzian model achieves a fitting accuracy of R2 > 0.996. Under the pressure conditions of 350 Torr, the fitting error for both the doublet and Voigt approximations remains below 0.3% for the D2 line and below 0.1% for the D1 line. At the pressures of 520 Torr and under elevated optical intensities, the spectrum evolves toward a single-peaked profile, rendering a single Lorentzian model sufficient. The quantitative applicability boundary of the doublet approximation in 87Rb vapor cells is established, defining the operational regime where hyperfine-resolved modeling can be reduced under collision-dominated conditions in NMRG systems.
We simulated the optical pumping rate of 87Rb atoms with Xe and high-pressure buffer gas in a cubic cell. We calculated absorption cross-section as a function of pumping laser frequency by considering a pressure and Doppler broadening as gas temperature varies from 364 K to 414 K. In a steady state the spin polarization and the atomic population of 87Rb atoms were obtained by optical pumping in each ground state. We calculated the optimum beam waist, linewidth and detuning of pumping beam to achieve higher population of polarized atoms at cell parameters such as temperature, size. We simulated that the optimum beam waist is 0.3 times of cubic cell length at 250 Torr of di-nitrogen and 50 Torr of Xe gas pressure. The optimum laser beam linewidth parabolically increases with increasing the temperature in range of few ten kelvin and it exponentially decrease with increasing the cubic cell length. We also observed that few ten GHz detuned laser frequency increases the optical pumping rate. These numerical results show appropriate experimental parameter as a function of cell temperature and size to get maximum population of spin polarized atoms in given temperature range.
The temperature of the alkali metal cell, which affects the density of the alkali-metal vapor and the gas pressure, is usually difficult to measure directly. However, the temperature of the alkali-metal cell and the density of the alkali-metal vapor are important parameters that affect the performance of the atomic sensor. In this paper, a device that can directly measure the internal temperature of an alkali metal cell in real time is designed for the first time to explore the relationship between alkali-metal vapor density and temperature. Alkali-metal vapor density is measured using the absorption spectrum. The pressure broadening model, combined with the transition of four hyperfine levels, was used to fit the absorption line of 87Rb D1 under the action of 700 Torr N2, and a good fitting effect was obtained. The experimental results show that the density of 87Rb is less than the value calculated by the empirical formula. Based on the experimental results, we give the calculation formula of 87Rb density with an uncertainty of only 4% and obtain the temperature dependence index of the line width and linear displacement of 87Rb in N2 by analyzing the absorption spectrum.
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.
Abstract In this work, we have investigated the transmission peak and absorption dip in the Doppler broadened V-type system using the D1 and D2 lines of 87Rb atoms in the presence of nitrogen buffer gas. The effects of the probe power variations at a fixed pump power on these resonances are examined both experimentally and theoretically. We have explored the fact that the transmission peak essentially turns into an absorption dip when the probe power is stronger than the pump power. Moreover, the theoretical model of a five-level V-type system is found to be sufficient to support the experimental outcomes when the effect of collision due to the presence of buffer gas is included in the theoretical model. We have also shown the variation of the resonance amplitude and population distribution in the upper level (|5〉) with increasing probe power.