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The time-of-flight mass spectrum of charged particles, which are created through two-step cw-laser photoionization of laser-cooled 87Rb atoms in an ion-neutral hybrid trap, is quantitatively investigated to further facilitate the study of Rb+-Rb reactive collisions. A microchannel plate (MCP) is used to detect charged particles, and two spectral peaks corresponding to the 87Rb+ ions and the product
$ \rm {}^{87}Rb_2^+ $ of the Rb+-Rb reaction were observed in the time-of-flight spectrum, respectively. The two peaks overlapped with each other and both showed an asymmetric profile. The information about the intensity, position, and half-width of the peak for a specific ion species was derived by fitting the time-of-flight spectrum with the probability density function of the Gumbel distribution. Then the relative ion intensity was converted into absolute ion number through the following steps. The rate equation of the total number of ions, which includes the number of atoms, the calibration factor of MCP, and the effective decay rate of ions in the ion trap, was established by modeling the photoionization of atoms. Combined with the absolute number of atoms measured by absorption imaging, the calibration factor in converting the ion intensity into the ion number was derived and the relative ion intensity was converted into the absolute number of ions. This provides a method of calibrating the MCP. The reliability of our calibration method was proved by the fact that the calibration factor in converting the intensity measured by MCP into particle number is independent of the duration of photoionization, the intensity and wavelength of the ionizing laser. Moreover, in order to explain the relationship between the peak width and temperature of the corresponding ion species, the time-of-flight spectra of the ions trapped in the ion trap were simulated by using COMSOL Multiphysics. The simulation results demonstrated that the large ion kinetic energy results in a narrow spectral peak. In sum, we quantitatively analyze and simulate the time-of-flight spectrum of the photoionization of cold atoms in the Rb+-Rb hybrid trap. The absolute number of ions is obtained by the intensity of the spectral peak, and the width of the spectral peak is related to the temperature of the ions. These results lay a foundation for the in-depth analysis of the ion-atom reaction collision and charged particle temperature relaxation in the photoionization of cold atoms, and thus further elucidating the subsequent collisional dynamics of ultracold plasmas.-
Keywords:
- ion-atom hybrid trap /
- low energy ion-atom reaction /
- time-of-flight spectrum /
- calibration factor
[1] Killian T C, Kulin S, Bergeson S D, Orozco L A, Orzel C, Rolston S L 1999 Phys. Rev. Lett. 83 4776
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[2] Killian T, Pattard T, Pohl T 2007 Phys. Rep. 449 77
Google Scholar
[3] Tomza M, Jachymski K, Gerritsma R, Negretti A, Calarco T, Idziaszek Z, Julienne P S 2019 Rev. Mod. Phys. 91 035001
Google Scholar
[4] 张栋栋, 童昕 2020 物理 49 241
Google Scholar
Zhang D D, Tong X 2020 Physics 49 241
Google Scholar
[5] Dieterle T, Berngruber M, Hölzl C, Löw R, Jachymski K, Pfau T, Meinert F 2021 Phys. Rev. Lett. 126 033401
Google Scholar
[6] Rellergert W G, Sullivan S T, Kotochigova S, Petrov A, Chen K, Schowalter S J, Hudson E R 2011 Phys. Rev. Lett. 107 243201
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[7] Hall F H J, Aymar M, Bouloufa-Maafa N, Dulieu O, Willitsch S 2011 Phys. Rev. Lett. 107 243202
Google Scholar
[8] Hall F H J, Eberle P, Hegi G, Raoult M, Aymar M, Dulieu O, Willitsch S 2013 Mol. Phys. 111 2020
Google Scholar
[9] Hall F H, Aymar M, Raoult M, Dulieu O, Willitsch S 2013 Mol. Phys. 111 1683
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[10] Sullivan S T, Rellergert W G, Kotochigova S, Hudson E R 2012 Phys. Rev. Lett. 109 223002
Google Scholar
[11] Härter A, Krükow A, Brunner A, Schnitzler W, Schmid S, Denschlag J H 2012 Phys. Rev. Lett. 109 123201
Google Scholar
[12] Krükow A, Mohammadi A, Härter A, Denschlag J H, Pérez-Ríos J, Greene C H 2016 Phys. Rev. Lett. 116 193201
Google Scholar
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Google Scholar
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Google Scholar
[15] Mohammadi A, Krükow A, Mahdian A, Deiß M, Pérez-Ríos J, da Silva H, Raoult M, Dulieu O, Hecker Denschlag J 2021 Phys. Rev. Research 3 013196
Google Scholar
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Google Scholar
[17] Sesko D W, Walker T G, Wieman C E 1991 J. Opt. Soc. Am. B 8 946
Google Scholar
[18] Paul W 1990 Rev. Mod. Phys. 62 531
Google Scholar
[19] Li X K, Zhang D C, Lv S F, Liu J Y, Jia F D, Wu Y, Lin X H, Li R, Xu X Y, Xue P, Liu X J, Zhong Z P 2020 J. Phys. B: At. Mol. Opt. Phys. 53 219501
Google Scholar
[20] Haan L D, Ferreira A 2006 Extreme Value Theory: an Introduction (New York; London: Springer) pp6–10
[21] Lee S, Ravi K, Rangwala S A 2013 Phys. Rev. A 87 052701
Google Scholar
[22] Liang W C, Jia F D, Wang F, Zhang X, Zhou J Y, Wang Y H, Qian J Y, Wang J G, Wu Y, Xue P, Zhong Z P 2022 arXiv: 2303.10360 [physics.atom-ph]
[23] 杜丽军 2014 博士学位论文 (武汉: 中国科学院武汉物理与数学研究所)
Du L J 2014 Ph.D. Dissertation (Wuhan: Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences) (in Chinese)
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图 1 典型飞行时间谱及其拟合曲线. 空心圆点代表实验获得的离子飞行时间谱. 虚线、点划线分别表示对离子飞行时间谱主峰、伴峰的拟合. 左Y轴代表微通道板(MCP)测量得到的离子信号强度, 右Y轴代表对MCP标定以后, 左Y轴的同一点对应的每时刻离子计数, 标定因子为
$ C_{{\rm{MCP}}} = 1.94\times10^{14} $ . 图中时间零点对应关闭离子阱、引导离子进入MCP的时刻Figure 1. Typical time-of-flight (TOF) spectra and the fitted curve. Hollow circle stands for the ion signal measured experimentally. Dashed line and dotted line are the fitted curve of first peak and second peak, respectively. Left Y-axis represents the ion signal measured by multichannel plate (MCP). Right Y-axis corresponds the calibrated ion count by the calibration factor
$ C_{{\rm{MCP}}} = $ $ 1.94\times10^{14} $ . The time zero is set to the moment when the ion trap was switched off and ions were guided to the MCP
图 2 连续光电离过程中冷原子数随光电离持续时间的变化及拟合曲线
Figure 2. Number of remaining atoms as a function of the duration of cw-laser photoionization and the fitted curve
图 3 实验测量的总离子数随光电离作用时间的变化及拟合曲线. 左Y轴对应实验测量得到的总离子相对强度, 右Y轴是对MCP标定以后, 左Y轴的同一点对应的绝对总离子数, 标定因子为
$ C_{\rm{MCP}} = 1.94\times10^{14} $ Figure 3. Measured total number of ions as a function of the duration ionization time and the fitted curve. Left Y-axis represents the relative ion intensity measured in experiments. Right Y-axis corresponds the calibrated absolute number of ions by the calibration factor of
$C_{\rm{MCP}} = 1.94\times10^{14}$ 
图 4 拟合得到微通道板的标定因子与电离光强度关系. 电离光波长分别为447, 463和478.8 nm
Figure 4. Fitted calibration factor for our microchannel plate (MCP) detector as the function of the intensity of ionizing laser. The wavelength of the ionizing laser are 447, 463 and 478.8 nm, respectively
图 5 使用COMSOL Multiphysics分别仿真离子阱囚禁10000, 20000, 50000, 100000个原子离子和分子离子时得到的飞行时间谱
Figure 5. Time-of-flight spectra of 10000, 20000, 50000 and 100000 Rb+ and Rb2+ simulated by COMSOL Multiphysics
图 6 实验测量的飞行时间谱及COMSOL Multiphysics仿真的飞行时间谱的比较. 实验谱在铷离子-铷原子混合阱的光电离过程测量得到, 电离光波长为478.8 nm, 强度为265.3 mW/cm2, 电离光作用在冷原子云的持续时间为500 ms. 仿真计算中, 考虑了
$ 10^5 $ 个铷原子离子和$ 10^5 $ 个铷分子离子, 带电粒子的初始温度的设置为20 mKFigure 6. Comparison between experimental and simulated TOF spectra by COMSOL Multiphysics. Experimental TOF spectra were measured in the photoionization process of our ion-atom hybrid trap. The wavelength and the intensity of the ionizing laser were 478.8 nm and 265.3 mW/cm2, respectively. The duration of photoionization was 500 ms. In the simulation,
$ 10^5 $ Rb+ and$ 10^5 $ $ {\rm Rb}_2^+ $ were added with an initial temperature of 20 mK -
[1] Killian T C, Kulin S, Bergeson S D, Orozco L A, Orzel C, Rolston S L 1999 Phys. Rev. Lett. 83 4776
Google Scholar
[2] Killian T, Pattard T, Pohl T 2007 Phys. Rep. 449 77
Google Scholar
[3] Tomza M, Jachymski K, Gerritsma R, Negretti A, Calarco T, Idziaszek Z, Julienne P S 2019 Rev. Mod. Phys. 91 035001
Google Scholar
[4] 张栋栋, 童昕 2020 物理 49 241
Google Scholar
Zhang D D, Tong X 2020 Physics 49 241
Google Scholar
[5] Dieterle T, Berngruber M, Hölzl C, Löw R, Jachymski K, Pfau T, Meinert F 2021 Phys. Rev. Lett. 126 033401
Google Scholar
[6] Rellergert W G, Sullivan S T, Kotochigova S, Petrov A, Chen K, Schowalter S J, Hudson E R 2011 Phys. Rev. Lett. 107 243201
Google Scholar
[7] Hall F H J, Aymar M, Bouloufa-Maafa N, Dulieu O, Willitsch S 2011 Phys. Rev. Lett. 107 243202
Google Scholar
[8] Hall F H J, Eberle P, Hegi G, Raoult M, Aymar M, Dulieu O, Willitsch S 2013 Mol. Phys. 111 2020
Google Scholar
[9] Hall F H, Aymar M, Raoult M, Dulieu O, Willitsch S 2013 Mol. Phys. 111 1683
Google Scholar
[10] Sullivan S T, Rellergert W G, Kotochigova S, Hudson E R 2012 Phys. Rev. Lett. 109 223002
Google Scholar
[11] Härter A, Krükow A, Brunner A, Schnitzler W, Schmid S, Denschlag J H 2012 Phys. Rev. Lett. 109 123201
Google Scholar
[12] Krükow A, Mohammadi A, Härter A, Denschlag J H, Pérez-Ríos J, Greene C H 2016 Phys. Rev. Lett. 116 193201
Google Scholar
[13] Krükow A, Mohammadi A, Härter A, Hecker Denschlag J 2016 Phys. Rev. A 94 030701
Google Scholar
[14] Dieterle T, Berngruber M, Hölzl C, Löw R, Jachymski K, Pfau T, Meinert F 2020 Phys. Rev. A 102 041301
Google Scholar
[15] Mohammadi A, Krükow A, Mahdian A, Deiß M, Pérez-Ríos J, da Silva H, Raoult M, Dulieu O, Hecker Denschlag J 2021 Phys. Rev. Research 3 013196
Google Scholar
[16] Lv S F, Jia F D, Liu J Y, Xu X Y, Xue P, Zhong Z P 2017 Chin. Phys. Lett. 34 013401
Google Scholar
[17] Sesko D W, Walker T G, Wieman C E 1991 J. Opt. Soc. Am. B 8 946
Google Scholar
[18] Paul W 1990 Rev. Mod. Phys. 62 531
Google Scholar
[19] Li X K, Zhang D C, Lv S F, Liu J Y, Jia F D, Wu Y, Lin X H, Li R, Xu X Y, Xue P, Liu X J, Zhong Z P 2020 J. Phys. B: At. Mol. Opt. Phys. 53 219501
Google Scholar
[20] Haan L D, Ferreira A 2006 Extreme Value Theory: an Introduction (New York; London: Springer) pp6–10
[21] Lee S, Ravi K, Rangwala S A 2013 Phys. Rev. A 87 052701
Google Scholar
[22] Liang W C, Jia F D, Wang F, Zhang X, Zhou J Y, Wang Y H, Qian J Y, Wang J G, Wu Y, Xue P, Zhong Z P 2022 arXiv: 2303.10360 [physics.atom-ph]
[23] 杜丽军 2014 博士学位论文 (武汉: 中国科学院武汉物理与数学研究所)
Du L J 2014 Ph.D. Dissertation (Wuhan: Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences) (in Chinese)
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