Chr. Tamm

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.

Experiments on one- and two-photon laser excitation of 232Th+ ions in a radiofrequency ion trap are reported. As the first excitation step, the strongest resonance line at 402 nm from the 6d^2 7s J=3/2 ground state to the 6d7s7p J=5/2 state at 24874 cm^{-1} is driven by radiation from an extended cavity diode laser. Spontaneous decay of the intermediate state populates a number of low-lying metastable states, thus limiting the excited state population and fluorescence signal obtainable with continuous laser excitation. We study the collisional quenching efficiency of helium, argon, and nitrogen buffer gases, and the effect of repumping laser excitation from the three lowest-lying metastable levels. The experimental results are compared with a four-level rate equation model, that allows us to deduce quenching rates for these buffer gases. Using laser radiation at 399 nm for the second step, we demonstrate two-photon excitation to the state at 49960 cm^{-1}, among the highest-lying classified levels of Th+. This is of interest as a test case for the search for higher-lying levels in the range above 55000 cm^{-1} which can resonantly enhance the excitation of the 229Th+ nuclear resonance through an inverse two-photon electronic bridge process.

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.

The 7.6-eV-isomer of Thorium-229 offers the opportunity to perform high resolution laser spectroscopy of a nuclear transition. We give a brief review of the investigations of this isomer. The nuclear resonance connecting ground state and isomer may be used as the reference of an optical clock of very high accuracy using trapped and laser-cooled thorium ions, or in a compact solid-state optical frequency standard of high stability.

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$^{-1}$.

We describe experimental investigations on an optical frequency standard based on a laser cooled 171Yb+ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the 2S1/2(F=0) ground state to the 2D3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two 171Yb+ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored 171Yb+ ions. The present experimental results indicate a relative instability (Allan standard deviation)of the optical frequency difference between the two systems of sigma_y(1000 s)=1.0E-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the 2D3/2 state of Yb+.

We experimentally investigate the resonance fluorescence spectrum of single 171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a radiofrequency trap. While the fluorescence scattering of 172Yb is continuous, the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing rate of spontaneous transitions leads to electron shelving in the metastable hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark periods can be varied by changing the intensity of a repumping laser field. Optical heterodyne detection is employed to analyze the fluorescence spectrum near the Rayleigh elastic scattering peak. It is found that the stochastic modulation of the fluorescence emission by quantum jumps gives rise to a Lorentzian component in the fluorescence spectrum, and that the linewidth of this component varies according to the average duration of the dark fluorescence periods. The experimental observations are in quantitative agreement with theoretical predictions.