B. Lipphardt

We present a scalable mixed-species Coulomb crystal clock based on the $^1S_0$ $\leftrightarrow$ $^3P_0$ transition in $^{115}$In$^+$. $^{172}$Yb$^+$ ions are co-trapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In$^+$-3Yb$^+$ crystal, achieving a relative systematic uncertainty of $2.5\times10^{-18}$ and a relative frequency instability of $1.6\times10^{-15}/\sqrt{τ/1\;\mathrm{s}}$. We report on absolute frequency measurements with an uncertainty of $1.3\times10^{-16}$ and optical frequency comparisons with clocks based on $^{171}$Yb$^+$ (E3) and $^{87}$Sr. With a fractional uncertainty of $4.4\times10^{-18}$, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the $^{115}$In$^+$/$^{87}$Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four $^{115}$In$^+$ clock ions, which reduces the instability to $9.2\times10^{-16}/\sqrt{τ/1\;\mathrm{s}}$.

We introduce a scheme to coherently suppress second-rank tensor frequency shifts in atomic clocks, relying on the continuous rotation of an external magnetic field during the free atomic state evolution in a Ramsey sequence. The method retrieves the unperturbed frequency within a single interrogation cycle and is readily applicable to various atomic clock systems. For the frequency shift due to the electric quadrupole interaction, we experimentally demonstrate suppression by more than two orders of magnitude for the ${}^2S_{1/2} \to {}^2D_{3/2}$ transition of a single trapped ${}^{171}\text{Yb}^+$ ion. The scheme provides particular advantages in the case of the ${}^{171}\text{Yb}^+$ ${}^2S_{1/2} \to {}^2F_{7/2}$ electric octupole (E3) transition. For an improved estimate of the residual quadrupole shift for this transition, we measure the excited state electric quadrupole moments $Θ({}^2D_{3/2}) = 1.95(1)~ea_0^2$ and $Θ({}^2F_{7/2}) = -0.0297(5)~ea_0^2$ with $e$ the elementary charge and $a_0$ the Bohr radius, improving the measurement uncertainties by one order of magnitude.

We experimentally investigate an optical frequency standard based on the $^2S_{1/2} (F=0)\to {}^2F_{7/2} (F=3)$ electric octupole (\textit{E}3) transition of a single trapped $^{171}$Yb$^+$ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy which reduces the related relative frequency uncertainty to $1.1\times 10^{-18}$. To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the \textit{E}3 transition as $0.888(16)\times 10^{-40}$ J m$^2$/V$^2$ and a dynamic correction $η(300~\text{K})=-0.0015(7)$. This reduces the uncertainty due to thermal radiation to $1.8\times 10^{-18}$. The residual motion of the ion yields the largest contribution $(2.1\times 10^{-18})$ to the total systematic relative uncertainty of the clock of $3.2\times 10^{-18}$.

We describe a measurement of the frequency of the 2S1/2(F = 0) - 2D3/2(F' = 2) transition of 171Yb+ at the wavelength 436 nm (frequency 688 THz), using a single Yb+ ion confined in a Paul trap and two caesium fountains as references. In one of the fountains, the frequency of the microwave oscillator that interrogates the caesium atoms is stabilized by the laser that excites the Yb+ reference transition with a linewidth in the hertz range. The stability is transferred to the microwave oscillator with the use of a fiber laser based optical frequency comb generator that also provides the frequency conversion for the absolute frequency measurement. The frequency comb generator is configured as a transfer oscillator so that fluctuations of the pulse repetition rate and of the carrier offset frequency do not degrade the stability of the frequency conversion. The phase noise level of the generated ultrastable microwave signal is comparable to that of a cryogenic sapphire oscillator. For fountain operation with optical molasses loaded from a laser cooled atomic beam source, we obtain a stability corresponding to a fractional Allan deviation of $4.1\times 10^{-14}\ (τ/\text{s})^{-1/2}$. With the molasses loaded from thermal vapor and an averaging time of 65 h, we measure the frequency of the Yb+ transition with a relative statistical uncertainty of $2.8\times10^{-16}$ and a systematic uncertainty of $5.9\times10^{-16}$. The frequency was also simultaneously measured with the second fountain that uses a quartz-based interrogation oscillator. The unperturbed frequency of the Yb+ transition is realized with an uncertainty of $1.1\times10^{-16}$ that mainly results from the uncertainty of the blackbody shift at the operating temperature near 300 K. The transition frequency of 688 358 979 309 307.82(36) Hz, measured with the two fountains, is in good agreement with previous results.

We experimentally investigate a recently proposed optical excitation scheme [V.I. Yudin et al., Phys. Rev. A 82, 011804(R)(2010)] that is a generalization of Ramsey's method of separated oscillatory fields and consists of a sequence of three excitation pulses. The pulse sequence is tailored to produce a resonance signal which is immune to the light shift and other shifts of the transition frequency that are correlated with the interaction with the probe field. We investigate the scheme using a single trapped 171Yb+ ion and excite the highly forbidden 2S1/2-2F7/2 electric-octupole transition under conditions where the light shift is much larger than the excitation linewidth, which is in the Hertz range. The experiments demonstrate a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations.

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition 2S1/2(F=0) -> F7/2(F=3) in a single trapped 171Yb+ ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f136s2 configuration of the upper state. The electric quadrupole moment of the 2F7/2 state is measured as -0.041(5) e(a0)^2, where e is the elementary charge and a0 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 7.1x10^(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.

We describe experiments with an optical frequency standard based on a laser cooled $^{171}$Yb$^+$ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the $^2S_{1/2}(F=0)$ ground state to the $^2D_{3/2}(F=2)$ state at the wavelength of 436 nm is used as the reference transition. In order to compare two $^{171}$Yb$^+$ standards, separate frequency servo systems are employed to stabilize two probe laser frequencies to the reference transition line centers of two independently stored ions. The experimental results indicate a relative instability (Allan standard deviation) of the optical frequency difference between the two systems of $σ_y(1000 {\rm s})=5\cdot 10^{-16}$ only, so that shifts in the sub-hertz range can be resolved. Shifts of several hertz are observed if a stationary electric field gradient is superimposed on the radiofrequency trap field. The absolute optical transition frequency of Yb$^+$ at 688 THz was measured with a cesium atomic clock at two times separated by 2.8 years. A temporal variation of this frequency can be excluded within a $1σ$ relative uncertainty of $4.4\cdot 10^{-15}$ yr$^{-1}$. Combined with recently published values for the constancy of other transition frequencies this measurement provides a limit on the present variability of the fine structure constant $α$ at the level of $2.0\cdot 10^{-15}$ yr$^{-1}$.