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 dependence on the excitation method (single Rabi pulse or two Ramsey pulses schemes) and the laser linewidth are discussed. The minimum Allan deviation that can be expected is estimated to σ y (τ ) ≈ 2.5 × 10 −15 / √ τ with τ the integration time. 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. If using the odd isotope 43 Ca + and a vessel cooled to 77 K, the expected relative shift is −2 × 10 −16 with an uncertainty of ±4 × 10 −16 , mainly due to the quadrupole shift induced by the unknown static electric field gradient .
A ring crystal of ions trapped in a linear multipole trap is studied as a basis for an optical frequency standard. The equilibrium conditions and cooling possibilities are discussed through an analytical model and molecular dynamics simulations. A configuration which reduces the frequency sensitivity to the fluctuations of the number of trapped ions is proposed. The systematic shifts for the electric quadrupole transition of calcium ions are evaluated for this ring configuration. This study shows that a ring of 10 or 20 ions allows to reach a short term stability better than for a single ion without introducing limiting long term fluctuations.
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