Zi Li

We present a detailed method for accumulating Ca$^{+}$ ions controllably in a linear Paul trap. The ions are generated by pulsed laser ablation and dynamically loaded into the ion trap by switching the trapping potential on and off. The loaded ions are precooled by buffer gas and then laser-cooled to form Coulomb crystals for verifying quantity. The number of ions is controlled by manipulating the trapping potential of the ion trap, partial pressure of buffer gas and turn-on time of the entrance end cap voltage. With single-pulse laser ablation, the number of trapped ions ranges from tens to ten thousand. The kinetic energy of loaded ions can be selected via the optimal turn-on time of the entrance end cap. Using multiple-pulse laser ablation, the number is further increased and reaches about $4 \times 10^{4}$. The dynamic loading method has wide application for accumulating low-yielding ions via laser ablation in the ion trap.

Thorium-229 possesses the lowest nuclear first excited state with an energy of about 8 eV. The extremely narrow linewidth of the nuclear first excited state with the uncertainty of 53 THz prevents the direct laser excitation and the realization of the nuclear clock. We present a proposal using the Coulomb crystal of a linear chain formed by the $^{229}$Th$^{3+}$ ions, the nuclei of $^{229}$Th$^{3+}$ ions in the ion trap are excited by the electronic bridge (EB) process. The 7$P_{1/2}$ state of the thorium-229 nuclear ground state is chosen for the EB excitation. Using the two-level optical Bloch equation under experimental conditions, we calculate that 2 out of 36 prepared thorium ions in the Coulomb crystal can be excited to the nuclear first excited state, and it takes about 2 hours to scan over the uncertainty of 0.22 eV. Taking the advantage of transition enhancement of the EB and the long stability of the Coulomb crystal, the energy uncertainty of the first excited state can be limited to the order of 1 GHz.