Abstract Optical clocks with ultralow uncertainty are strong candidates for the next redefinition of the SI second. The 171 Yb + single-ion clock is particularly attractive owing to its two clock transitions (E2 and E3) and its potential for low uncertainty. A major contribution to the uncertainty budget arises from the electric-quadrupole shift, caused by the interaction between the atomic quadrupole moment and the electric-field gradient at the trap center and strongly dependent on the orientation of the quantization axis. To evaluate this shift, a simplified orthogonal magnetic-field method was employed: three mutually orthogonal magnetic-field directions are generated together with an auxiliary non-orthogonal field. With a dual-condition locking scheme, we measure the E2 transition frequency differences between magnetic-field configurations, infer the electric-field gradient, and apply corrections for the associated quadratic Zeeman shifts. The uncertainty due to magnetic-field misalignment is quantified using a calibrated current-to-field model. The resulting electric-quadrupole shift correction for the 2 S 1/2 → 2 F 7/2 (E3) transition is 3.24 mHz, corresponding to a fractional uncertainty of 1.1×10 −18 in the absolute frequency measurement.
Compared to other stable isotopes of
Yb+,
173Yb+ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped
173Yb+ ion. The previously unobserved
2S1/2→2D3/2 electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between
171Yb+ and
173Yb+ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the
2D3/2 state with a relative uncertainty below
10−8. From the HFS measurement data, we infer for
173Yb a nuclear magnetic octupole moment
Ω=−0.062(8)(b×μN) with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the
2S1/2 and
2D3/2 states.
An optical clock based upon a single mercury ion in a radio-frequency trap has the potential for both high stability and high accuracy. The systematic uncertainty of this frequency standard is limited by contributions due to two types of external fields. The clock has previously been operated with a magnetic bias field that destabilizes dark states that limit the rates of laser cooling and state detection. This bias field has previously resulted in a substantial second-order Zeeman shift. We now destabilize the dark states with a polarization-scrambling technique that allows us to operate with only a minimal magnetic field. The second uncertainty that we address here is the magnitude of the quadrupole shift due to the interaction of stray electric-field gradients with the quadrupole moment of the ion. We describe the steps that we are taking to evaluate this shift in the near future. 1
We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.
We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals and impose one of the limitations forcing current optical ion clocks to work with a single probe ion. Canceling this shift, at each interrogation cycle of the ion frequency, reduces the complexity in using N>1 ions in clocks, thus allowing for a reduction of the instability in the clock frequency by sqrt[N] according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven ^{88}Sr^{+} ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to the ≈10 mHz level where other shifts, such as the relativistic second-order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of first-order Zeeman shifts.