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 report the first operation of a
Ra+ optical clock, a promising high-performance clock candidate. The clock uses a single trapped
226Ra+ ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the
D5/2 state to the
S1/2 state Land\'e
g-factors:
gD/gS=0.598 805 3(11). A
Ra+ optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.
We demonstrate that several metastable excited states in Hf ii, Hf iv, and W vi ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. The cooling electric dipole (
E1) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using
Ca+ or
Sr+ ions. Energy levels; Land\'e
g factors; transition amplitudes for electric dipole (
E1), electric quadrupole (
E2), and magnetic dipole (
M1) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory (
CI+SD), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches
K=8.3. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.
Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .
We demonstrate transition between the fine structure splitting of the ground state of triply ionized zirconium (Zr IV) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition and can be accessible by a readily available laser. We suggest to consider stable even isotopes of Zr and
MJ=±1/2 sublevels (i.e.
∣4D3/2,MJ=±1/2⟩→∣4D5/2,MJ=±1/2⟩ clock transition) for the experimental advantage. By performing necessary calculations, we have estimated possible systematics due to blackbody radiation, ac Stark, electric quadrupole and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock can be very useful in quantum thermometry and frequency metrology.
We investigate the feasibility of precision frequency metrology with large ion crystals. For clock candidates with a negative differential static polarizability, we show that micromotion effects should not impede the performance of the clock. Using
Lu+ as a specific example, we show that quadrupole shifts due to the electric fields from neighboring ions do not significantly affect clock performance. We also show that effects from the tensor polarizability can be effectively managed with a compensation laser at least for a small number of ions ($\ensuremath{\lesssim}{10}^{3}$). These results provide new possibilities for ion-based atomic clocks, allowing them to achieve stability levels comparable to neutral atoms in optical lattices and a viable path to greater levels of accuracy.