Sympathetic crystallization of CaH${}^{+}$ produced by a laser-induced reaction

We investigated sympathetic Coulomb crystallization of CaH${}^{+}$ ions produced by a laser-induced reaction through an excited state according to ${}^{40}\mathrm{Ca}$${}^{+}$($4p\hspace{0.5em}{}^2{P}_{1/2}$) $+$ ${\mathrm{H}}_2$ $\to$ ${}^{40}\mathrm{Ca}$H${}^{+}$ $+$ H. ${}^{40}\mathrm{Ca}$H${}^{+}$ ions stored in a linear Paul trap were characterized by their secular-motion excitation spectrum and by the modified fluorescence images of crystallized Ca${}^{+}$ ions. The number of two-species crystallized ions, the secular motion temperature, and the structure were determined by molecular dynamics simulations. Both the observed two-species ion crystals and simulation images demonstrate that the CaH${}^{+}$ ions were sympathetically crystallized with their secular-motion temperature being less than 10 mK. We determined reaction rates from fluorescence images of two-species Coulomb crystals by systematically changing the reaction time. In addition a lower limit for the reaction rate coefficient $k=8\times {10}^{-10}$ cm${}^3$/s was obtained.

Figure 1

A secular-motion-excitation mass spectrum of a two-species Coulomb crystal and the snapshots of the fluorescence images corresponding to states (1)–(4) in the mass spectrum. The exposure time of the CCD camera was set to 1 s. The reaction time for producing CaH${}^{+}$ ions was $3.2\times {10}^2$ s. We applied a strong perturbation voltage of 35 mV for secular-motion excitation.

Figure 2

(a) A two-species ion Coulomb crystal consisting of Ca${}^{+}$ and CaH${}^{+}$. The upper side of the image is occupied by CaH${}^{+}$ ions. The rf frequency and the amplitude are $f_{\mathrm{rf}}=5.49$ MHz and $V_{\mathrm{ac}}=171.5$ V, respectively. The static voltage applied to the end electrodes is $V_z=7.1$ V. (b) A simulation image reproducing the image (a). The numbers of Ca${}^{+}$ and CaH${}^{+}$ are determined to be $N({\mathrm{Ca}}^{+})=134$ and $N({\mathrm{CaH}}^{+})=40$, respectively. The correction static fields of $E_x=40$ mV/mm and $E_y=-40$ mV/mm were added to reproduce the asymmetric image (a). The secular-motion temperature of both ion species is computed to be about 7 mK.

Figure 3

Observed fluorescence images (left) of two-species Coulomb crystals with a small number of ions and the corresponding simulation results (right). The scale of all figures is the same. From the results of the MD simulation, the ion numbers and the upper limit of the secular motion temperature are determined: (a) $N({\mathrm{Ca}}^{+})=28$, $N({\mathrm{CaH}}^{+})=7$, $T_{\sec }⩽5$ mK; (b) $N({\mathrm{Ca}}^{+})=7$, $N({\mathrm{CaH}}^{+})=1$, $T_{\sec }⩽8$ mK.

Figure 4

Systematic observation of fluorescence images of two-species ion Coulomb crystals during reaction (1). In the initial condition a prolate Ca${}^{+}$ Coulomb crystal was produced. As the reaction time increased the dark area in the upper side of the crystal extended. The nominal ${\mathrm{H}}_2$ pressure was $4.8\times {10}^{-6}$ Pa during the measurement. Observation optics with a magnification of 3$\times$ was used.

Figure 5

(a) The decay of the relative number of Ca${}^{+}$ ions in the large ion crystal of Fig. 4 due to the laser-induced reaction (1). The relative number of Ca${}^{+}$ ions is obtained by estimating the volume of the fluorescence images in Fig. 4. It is clearly seen that the slope of the decay curve changes at about 400 s. (b) A least-square fit analysis of the initial slope yields the reaction rate. The error is estimated by the uncertainties of the volume determination of the Ca${}^{+}$ crystals. The data at reaction times less than 400 s in panel (a) was used. A reaction rate of $(1.9\pm 0.8)\times {10}^{-4}$ ${\mathrm{s}}^{-1}$ was obtained.

Figure 6

Systematic observation of fluorescence images of two-species small Coulomb crystals. The images were observed using the lens system with 10$\times$ magnification. The corresponding simulation images are also shown in the lower images (b). The reaction time and the assumed secular-motion temperatures in the MD simulations are indicated in the images. During the measurements the nominal pressure of the ${\mathrm{H}}_2$ gas was $4.8\times {10}^{-6}$ Pa. The rf frequency and the amplitude are $f_{\mathrm{rf}}=5.532$ MHz and $V_{\mathrm{ac}}=204.5$ V, respectively. The static voltage applied to the end electrodes is $V_z=5.3$ V.

Figure 7

A plot of the ion numbers of Ca${}^{+}$ and CaH${}^{+}$ contained in the Coulomb crystals as a function of the reaction time. Each point was determined by fitting simulation images to the observed images in Fig. 6. The error of the number of ions is caused by the uncertainty of the fitting results. The uncertainty of the reaction time (typically $\pm$25 s) is the time taken for loading and evacuating the ${\mathrm{H}}_2$ gas. The solid line for Ca${}^{+}$ is the best-fitting exponential curve to sets of the data while the line for CaH${}^{+}$ is just to guide the eye. The reaction rate of $(6.1\pm 0.2)\times {10}^{-4}$ ${\mathrm{s}}^{-1}$ was obtained by the Ca${}^{+}$ decay rate.

Figure 8

A plot of the reaction rates as a function of the 397-nm laser detuning. The initial numbers of Ca${}^{+}$ ions were determined by the same method described in the text: (a) $74\pm 2$, (b) $66\pm 2$, (c) $94\pm 2$, (d) $(8.1\pm 0.2)\times {10}^3$, (e) $(7.3\pm 0.2)\times {10}^3$, and (f) $(5.8\pm 0.1)\times {10}^3$. The nominal pressure of ${\mathrm{H}}_2$ (4.8$\times$10${}^{-6}$ Pa) is the same for all measurements. The error bars originate from the fitting error of the exponential curve. The error of (e) is $\pm 1\times {10}^{-5}$, which is within the point size.