Sub-hertz optical frequency metrology using a single ion of 171Yb+

Optical frequency standards offer the possibility of a step improvement of up to two orders of magnitude in the accuracy with which the SI second can be realised. 171Yb+ possesses two dipole-forbidden optical transitions that are promising candidates for a redefinition of the second. In this thesis, absolute frequency measurements of these two transitions are presented. A number of experimental upgrades have been implemented, which have resulted in a large reduction in both the statistical and systematic uncertainties associated with the measurements and have improved both the reliability and simplicity of the experimental setup. In particular, the replacement of two frequency-doubled Ar+-pumped Ti:sapphire lasers with extended cavity diode lasers has eliminated the downtime associated with their maintenance. Additionally, the introduction of polarisation modulation on the cooling light has allowed the residual bias magnetic field required for laser cooling to be reduced by a factor of thirty. The first measurement at the National Physical Laboratory (NPL) of the frequency of the 2S1/2 (F = 0) → 2D3/2 (F′ = 2) electric quadrupole (E2) transition at 436 nm is presented. The transition frequency was measured against a hydrogen maser using a femtosecond optical frequency comb, and was determined with a relative standard uncertainty of 1.3 × 10−14. A commercial diode-based laser system was then implemented in order to drive the 2S1/2 (F = 0) → 2F7/2 (F′ = 3) electric octupole (E3) transition at 467 nm. The laser frequency was actively stabilised to the ultra-narrow atomic absorption with a resolved linewidth of 11 Hz, allowing the acquisition of ninety hours of frequency data measured relative to the NPL’s primary frequency standard CsF2. Combined with a thorough evaluation of the systematic perturbations, the total fractional uncertainty in the absolute frequency of the transition has been reduced by a factor of twenty to 1 × 10−15. Recent complementary results from Physikalisch-Technische Bundesanstalt (PTB) show that the E3 transition in 171Yb+ has the potential to be a highly accurate and reproducible optical frequency standard, and to date these measurements demonstrate the best international agreement between trapped ion optical frequency standards.