Sub-Hertz Optical Frequency Comparisons between Two TrappedYb+171Ions

Abstract

We compare the frequencies of the 6s2S(1/2)(F = 0)-->5d2D(3/2)(F = 2) reference transition in 171Yb+ for two single ions stored in independent traps. The quadrupole moment of the 5d2D(3/2) state is measured to be 9.32(48) x 10(-40) C m2 and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be alphaS(S(1/2)) - alphaS(D(3/2)) = -6.9(1.4) x 10(-40) J m2/V2 and alphaT(D(3/2)) = -13.6(2.2) x 10(-40) J m2/V2, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of 3.8(6.1) x 10(-16). This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

Optical Atomic Coherence at the 1-Second Time Scale

“…Enhancing their ratio, which is equivalent to improving spectral resolving power, characterizes much of the recent progress in these fields. Trapped ions have so far provided the best platform for research along this direction, resulting in a number of seminal achievements (3)(4)(5)(6)(7)(8). The principal advantage of the ion system lies in the clean separation between the internal atomic state and the external center-of-mass motion, leading to long coherence times associated with both degrees of freedom.…”

Quantum physics exploring gravity in the outer solar system: the SAGAS project

“…Instead of the microwave frequencies used in PHARAO, the SAGAS clock uses optical frequencies. Ground based optical clocks are evolving at a significantly fast rate, with one or two single ion clocks already demonstrating instabilities ∼4 × 10 −17 at < 10 4 s and 2 × 10 −17 accuracy in realising the unperturbed ion frequency [37][38][39][40][41]. There is good reason to expect similar performance for a range of other optical clock systems, which is extendable to below the target specification at longer times.…”

Ion-trajectory analysis for micromotion minimization and the measurement of small forces

“…If constant rf power is mandatory, the method presented here can also be carried out by a variation of a dc voltage bias applied to the rf or dc electrodes instead of the rf power variation [42]. Under variation of a dc bias symmetrically applied to the rf or dc electrodes, the rf trap frequencies will remain constant, while the dc trap frequencies change.…”

“…Method ∆ε (V/m) [33] Photon-correlation spectroscopy 0.9 [3] / [38] / [37] Micromotional sideband spectroscopy 7 / 1 / 0.4 [40] Ion-cavity emmission spectroscopy 1.8 [45] / [44] Parametric excitation of secular motion 6 / 0.4 [31] Neutral atom loss 0.02 [42] Monitor displacement ≤ 11.8 This work…”

“…Excess micromotion is detected by monitoring the ion's average position while changing the strength of the effective trapping potential using either dc fields [42] or changing the rf voltage amplitude [35].…”