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

Abstract

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 .

Laser frequency stabilization to a single ion

“…While a final optimization will also have to take the specific frequency noise properties of the probe laser into account, these general results are meant to provide initial guidance in the selection of suitable experimental parameters. During the preparation of the manuscript two related studies were published [12,13] and we will comment on the relation to that work at the end of section (3).…”

Absolute Frequency Measurement of theCa+404s S1/2Chwalla1, Benhelm2, Kim3 et al. 2009Phys. Rev. Lett.16151240View full textAdd to dashboardCite

“…Experiments with single, trapped ions have provided key contributions to the field of optical clocks and precision measurements in the past 20 years [3]. Several candidates for an optical ion clock have been investigated such as Hg + , Al + , Yb + , In + , Sr + [4,5,6,7,8,9], or proposed like Ca + [10,11].…”

Direct frequency-comb spectroscopy of a dipole-forbidden clock transition in trapped Ca^+40 ions

“…removed by increasing the confinement of the ions by the trap such that the Lamb-Dicke regime is attained [17]. In addition, hertz-level FC linewidths may be achieved by locking to a high-finesse cavity [5].…”

“…The theory on further experimental requirements are described in [17] and shown to be experimentally achievable by [13].…”