Direct Laser Cooling Al${}^{+}$ Ion Optical Clocks

The Al ${}^{+}$ ion optical clock is a very promising optical frequency standard candidate due to its extremely small black-body radiation shift. It has been successfully demonstrated with the indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al ${}^{+}$ ion optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme, two Al ${}^{+}$ traps are utilized. The first trap is used to trap a large number of Al ${}^{+}$ ions to improve the stability of the clock laser, while the second trap is used to trap a single Al ${}^{+}$ ion to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach $9.0\times {10}^{-17}/\sqrt{\tau }$. For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about $1\times {10}^{-18}$. The proposed Al ${}^{+}$ ion optical clock has the potential to become the most accurate and stable optical clock. (paper)