Analysis and simulation of time-of-flight spectrum in Rb⁺-Rb hybrid trap

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 \begin{document}$ \rm {}^{87}Rb_2^+ $\end{document} 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.