Evaluation of the ultimate performances of a Ca+ single-ion frequency standard

We numerically evaluate the expected performances of an optical frequency standard at 729 nm based on a single calcium ion. The frequency stability is studied through the Allan deviation and its dependance on the excitation scheme (single or two-Ramsey pulses). The minimum Allan deviation that can be expected is estimated to $\sigma_y(\tau) \approx 3.4\times 10^{-15}/\sqrt{\tau}$. The frequency shifts induced by the environmental conditions are evaluated to minimize the uncertainty of the proposed standard by chosing the most suited environment for the ion. The expected relative shift is $-2 \times 10^{-16}$ with an uncertainty of $\pm 3\times10^{-16}$, if using the odd isotope $^{43}$Ca$^{+}$.