We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to 1$\times10^{-17}$ and below. We calculated a.c. polarizabilities of the $5s^2 ^1S_0$ and $5s5p ^3P_0^o$ clock states that are important for reducing the uncertainty of blackbody radiation-induced frequency shifts for the $^1S_0 - ^3P_0^o$ clock transition. We determined four low-lying even-parity states whose total contribution to the static polarizability of the $^3P_0^o$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^3P_0^o$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below 1$\times10^{-17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.
In the recent work [A.~Yamaguchi et. al, Phys. Rev. Lett. {\bf 123}, 113201 (2019)] Cd has been identified as an excellent candidate for a lattice clock. Here, we carried out computations needed for further clock development and made an assessment of the higher-order corrections to the light shift of the $5s^2\, ^1\!S_0$--$5s5p\, ^3\!P_0^o$ clock transition. We carried out calculations of the magnetic dipole and electric quadrupole polarizabilities and linear and circular hyperpolarizabilities of the $5s^2\, ^1\!S_0$ and $5s5p\, ^3\!P_0^o$ clock states at the magic wavelength and estimated unc…
We study a wide range of neutral atoms and ions suitable for ultra-precise atomic optical clocks with naturally suppressed black body radiation shift of clock transition frequency. Calculations show that scalar polarizabilities of clock states cancel each other for at least one order of magnitude for considered systems. Results for calculations of frequencies, quadrupole moments of the states, clock transition amplitudes and natural widths of upper clock states are presented.
We report a frequency measurement of the 1S0-3P0 transition of 87Sr atoms in an optical lattice clock. The frequency is determined to be 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall. Two previous measurements of this transition were found to disagree by about 2x10^{-13}, i.e. almost four times the combined error bar, instilling doubt on the potential of optical lattice clocks to perform at a high accuracy level. In perfect agreement with one of these two values, our measurement essentially dissipa…
The quadratic Zeeman shift coefficient of 3P0 clock state for strontium is determined in theory and experiment. In theory, we derived the expression of the quadratic Zeeman shift of 3P0 clock state for 88Sr and 87Sr in the weak-magnetic-field approximation. By using the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. To determine the calculated results, the quadratic Zeeman shift coefficient of 3P0,F=9/2,MF=+/-9/2 clock state was measured in our 87Sr optical lattice clock. The calculated results C2=-23.38(5) MHz/T2 for 88Sr and the 3P0,F=…
We have developed an all-particle Fock-space relativistic coupled-cluster method to calculate the properties of two-valence atoms and ions. Using the method we compute the properties associated with hyperfine induced $^1S_0 - ^3P^o_0$ clock transition in Al$^+$. Our result of the $^3P^o_0$ metastable state life time, $20.20 \pm 0.91$ s, is in excellent agreement with the experimental value, $20.60 \pm 1.4$ s [Phys. Rev. Lett. {\bf 98}, 220801 (2007)]. Our studies show that the contributions from the triple excitations, and the corrections from the Breit interaction and QED effects are essentia…
We have performed ab initio calculations of the frequency shift induced by a static electric field on the cesium clock hyperfine transition. The calculations are used to find the frequency shifts due to blackbody radiation. Our result ($δν/E^2=-2.26(2)\times 10^{-10}$Hz/(V/m)$^2$) is in good agreement with early measurements and ab initio calculations performed in other groups. We present arguments against recent claims that the actual value of the effect might be smaller. The difference ($\sim$ 10%) between ab initio and semiempirical calculations is due to the contribution of the continuum s…
A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. We present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5$\times$10${}^{-19}$.
Optical clocks are not only powerful tools for prime fundamental research, but are also deemed for the re-definition of the SI base unit second as they now surpass the performance of caesium atomic clocks in both accuracy and stability by more than an order of magnitude. However, an important obstacle in this transition has so far been the limited reliability of the optical clocks that made a continuous realization of a timescale impractical. In this paper, we demonstrate how this situation can be resolved and that a timescale based on an optical clock can be established that is superior to on…
Relativistic configuration-interaction and coupled-cluster calculations of Ir$^{17+}$ transition energies and properties for optical clock applications
By use of the \textsc{grasp2018} package we perform Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) for the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ levels in neutral cadmium and mercury. By supplying the resultant atomic state functions to the \textsc{ris4} program, we evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$ (clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We make revised estimates of the nuclear charge parameters $λ^{A,A'}$ and differences in mean-square charge radii $δ\langle r^2\rangle^{A,A'}$ for b…
We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the static dipole polarizabilities of the ground and first excited states of Al+ have been determined to precisely estimate the uncertainty associated with the BBR shift of its clock frequency measurement. The obtained relative BBR shift is -3.66+-0.44 for the 3s^2 ^1S_0^0 --> 3s3p ^3P_0^0 transition in Al+ in contrast to the value obtained in the latest clock frequency measurement, -9+-3 [Phys. Rev. Lett. 104…
We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar $M1$ and $E2$ atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We have developed an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows to effectively and accurately carry out complete summations over intermediate states. We applied our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carried out an accurate calculation of th…
Aided by ultra-high resolution spectroscopy, the overall systematic uncertainty of the $^{1}S_{0}$-$^{3}P_{0}$ clock resonance for lattice-confined $^{87}$Sr has been characterized to $9\times10^{-16}$. This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429,228,004,229,874.0(1.1) Hz, where the $2.5\times10^{-15}$ fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency…
We have developed a broadly-applicable approach that drastically increases the ability to accurately predict properties of complex atoms. We applied it to the case of Ir$^{17+}$, which is of particular interest for the development of novel atomic clocks with high sensitivity to the variation of the fine-structure constant and dark matter searches. The clock transitions are weak and very difficult to identity without accurate theoretical predictions. In the case of Ir$^{17+}$, even stronger electric-dipole (E1) transitions eluded observation despite years of effort raising the possibility that …
We report a vapor-cell magneto-optical trapping of Hg isotopes on the ${}^1S_0-{}^3P_1$ intercombination transition. Six abundant isotopes, including four bosons and two fermions, were trapped. Hg is the heaviest non-radioactive atom trapped so far, which enables sensitive atomic searches for ``new physics'' beyond the standard model. We propose an accurate optical lattice clock based on Hg and evaluate its systematic accuracy to be better than $10^{-18}$. Highly accurate and stable Hg-based clocks will provide a new avenue for the research of optical lattice clocks and the time variation of t…
We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of th…
Time and frequency are the most accurately measurable quantities, providing foundations for science and modern technologies. The accuracy relies on the SI (Systéme International) second that refers to Cs microwave clocks with fractional uncertainties at $10^{-16}$. Recent revolutionary progress of optical clocks aims to achieve $1\times 10^{-18}$ uncertainty, which however has been hindered by long averaging-times or by systematic uncertainties. Here, we demonstrate optical lattice clocks with $^{87}$Sr atoms interrogated in a cryogenic environment to address the blackbody radiation-induced fr…
Black-body radiation (BBR) shifts of $^3\!P_0-^1\!S_0$ clock transition in divalent atoms Cd and Zn are evaluated using accurate relativistic many-body techniques of atomic structure. Static polarizabilities of the clock levels and relevant electric-dipole matrix elements are computed. We also present a comparative overview of the BBR shifts in optical clocks based on neutral divalent atoms trapped in optical lattices.
We present an experiment to characterize our new linear ion trap designed for the operation of a many-ion optical clock using 115-In^+ as clock ions. For the characterization of the trap as well as the sympathetic cooling of the clock ions we use 172-Yb^+. The trap design has been derived from finite element method (FEM) calculations and a first prototype based on glass-reinforced thermoset laminates was built. This paper details on the trap manufacturing process and micromotion measurement. Excess micromotion is measured using photon-correlation spectroscopy with a resolution of 1.1nm in moti…
A calculation of the blackbody radiation shift of the B$^+$ clock transition is performed. The polarizabilities of the B$^+$ $2s^2$ $^1$S$^e$, $2s2p$ $^1$P$^o$, and $2s2p$ $^3$P$^o$ states are computed using the configuration interaction method with an underlying semi-empirical core potential. The recommended dipole polarizabilities are 9.64(3) $a_0^3$, 7.78(3) $a_0^3$ and 16.55(5) $a_0^3$ respectively. The derived frequency shift for the $2s^2$ $^1$S$^e$ $\to$ $2s2p$ $^3$P$^o_0$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation (Sa…
Singly ionised Lutetium has recently been suggested as a potential clock candidate. Here we report a joint experimental and theoretical investigation of \ce{Lu^+}. Measurements relevant to practical clock operation are made and compared to atomic structure calculations. Calculations of scalar and tensor polarizabilities for clock states over a range of wavelengths are also given. These results will be useful for future work with this clock candidate.
We study the Ho$^{14+}$ ion as a candidate for extremely accurate and stable optical atomic clock which is sensitive to the time variation of the fine structure constant. We demonstrate that the proposed system has all desired features including relatively strong optical electric dipole and magnetic dipole transitions which can be used for cooling and detection. Zero quadrupole moments for the relevant states in the clock transition allows interrogating multiple ions to improve the clock stability.
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of m_q/Lambda_{QCD} from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Hg+ and optical transtion in Hg+.
An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the $5s^2 {}^1S_0 \to 5s5p {}^3P_0$ transition of ${}^{87}{\rm Sr}$ atoms as a "clock transition". Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than $ 10^{-17}$.
Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisi…
It is shown that the dynamic differential scalar polarisability of the $S_{1/2}-D_{5/2}$ transition in $^{138}$Ba$^+$ can be determined to an inaccuracy below $0.5\%$ across a wide wavelength range ($λ>700\,\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-stark shift of the clock transition would then provide an \emph{in situ} measurement of the laser's intensity to the same $0.5\%$ level of inaccuracy, which is not ea…
We present precise values of the dipole polarizabilities ($α$) of the ground $\rm [4f^{14}6s] ~ ^2S_{1/2}$ and metastable $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states of Yb$^+$, that are %vital {\bf important} in reducing systematics in the clock frequency of the $\rm[4f^{14}6s] ~ ^2S_{1/2} \rightarrow [4f^{14}5d] ~ ^2D_{3/2}$ transition. The static values of $α$ for the ground and $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states are estimated to be $9.8(1) \times 10^{-40} \,\,\rm Jm^2V^{-2}$ and $17.6(5) \times 10^{-40}\,\, \rm Jm^2V^{-2}$, respectively, while the tensor contribution to the $\rm [4f^{14} 5d] ~…
In this paper, we propose a scheme of active ion optical clock with detailed pumping method, lasing states, output power, linewidth and light shift. Using 171Yb+ ions in a Paul Trap we propose to utilize a Fabry-Perot resonator to realize lasing of active optical frequency standards. The quantum-limited linewidth of active 171Yb+ ion optical clock is narrower than 1 mHz. Based on the mechanism and advantages of active optical clock at ion optical clock transition frequency, this new laser light source as a stable local oscillator, will be beneficial to the single-ion optical clock, which curre…
We propose a novel class of atomic clocks based on highly charged ions. We consider highly-forbidden laser-accessible transitions within the $4f^{12}$ ground-state configurations of highly charged ions. Our evaluation of systematic effects demonstrates that these transitions may be used for building exceptionally accurate atomic clocks which may compete in accuracy with recently proposed nuclear clock.
Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly-charged ions (HCIs) made HCIs accessible for high resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in the Cf$^{15+}$ and Cf$^{17+}$ ions. Using a high-accuracy relativistic method of calculation we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric …
Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequenc…
We analyze both the s- and p-wave collision induced frequency shifts and propose a over-$π$ pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over-$π$ pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of $10^{-18…
We investigate roles of electron correlation effects in the determination of $g_j$ factors of the $ns~^2S_{1/2}$ ($n$=5,6,7), $np~^2P_{1/2,3/2}$ ($n$=5,6), $5d~^2D_{3/2,5/2}$, and $4f~^2F_{5/2,7/2}$ states of the singly ionized cadmium (Cd$^+$) ion. Single and double excited configurations along with important valence triple excited configurations through relativistic coupled-cluster (RCC) theory are taken into account for incorporating electron correlation effects in our calculations. We find significant contributions from the triples to the lower $S$ and $P$ states for attaining high accurac…
We demonstrate state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in the optical lattice. A magic wavelength of the proposed |7S1/2; F = 4, MF = 0> - |6P3/2; F = 3, MF = 0> clock transition in Cs atom is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about 10-15 level to the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. Th…
We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground $6s^2 ^1S_0$ and the first excited $6s6p ^3P^o_0$ states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the $6s^2 ^1S_0 - 6s6p ^3P^o_0$ transition. We determine (i) the first four {\em magic} wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the forth magic waveleng…
Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in $10^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as variation of fundamental constants, violation of the local Lorentz invariance, and forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of so…
Relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) are carried out for the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ states in neutral ytterbium by use of the available GRASP2018 package. From the resultant atomic state functions and the RIS4 extension, we evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$ (clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We present improved estimates of the nuclear charge parameters, $λ^{A,A'}$, and differences in mean-square charge radii, $δ\langle r^2\rangle^{A,A'}$, an…
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of the ratio of quark mass and strong interaction scale (m_q/Lambda_{QCD}) from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Yb+, Hg+ and optical transition in Hg+. Experiments with Cd+, deuterium/hydrogen, molecule SF_6, Zeeman transitions in He_3/Xe are also discussed.
We demonstrate agreement between measurements and ab initio calculations of the frequency shifts caused by distributed cavity phase variations in the microwave cavity of a primary atomic fountain clock. Experimental verification of the finite element models of the cavities gives the first quantitative evaluation of this leading uncertainty and allows it to be reduced to delta nu / nu = 8.4\times10^-17. Applying these experimental techniques to clocks with improved microwave cavities will yield negligible distributed cavity phase uncertainties, less than \pm1\times10^-17.
We identify laser-accessible transitions in group 16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground $^{3}P_{J}$ fine structure manifold exhibits irregular (nonmonotonic in $J$) energy ordering for large enough ionization degree. We consider the $|^3P_2\rangle \longleftrightarrow |^3P_0\rangle$ (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are …
The blackbody radiation shift of the Ga$^+$ $4s^2 \ ^1S^e_0 \to 4s4p \ ^3P^o_0$ clock transition is computed to be $-$$0.0140 \pm 0.0048$ Hz at 300 K. The small shift is consistent with the blackbody shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga$^+$ $4s^2 \ ^1S^e_0$, $4s4p \ ^3P^o_0$, and $4s4p \ ^1P^o_1$ states were computed using the configuration interaction method with an underlying semi-empirical core potential. A byproduct of the analysis involved large scale calculations of the low lying spectrum and oscillator streng…
We study the $^1$S$_0 - ^3$D$_2$ and $^1$S$_0 - ^3$D$_3$ transitions in Cu II and the $^1$S$_0 - ^3$P$^{\rm o}_2$ transition in Yb III as possible candidates for the optical clock transitions. A recently developed version of the configuration (CI) method, designed for a large number of electrons above closed-shell core, is used to carry out the calculation. We calculate excitation energies, transition rates, lifetimes, scalar static polarizabilities of the ground and clock states, and blackbody radiation shift. We demonstrate that the considered transitions have all features of the clock trans…
We propose here a few selective highly charged ions (HCIs), namely Ni$^{12+}$ and Cu$^{13+}$, Pd$^{12+}$ and Ag$^{13+}$, that not only promise to be very high accurate optical clocks below $10^{-19}$ uncertainties, but also offer quality factors larger than $10^{15}$ and yet possess simple atomic structures for the experimental set-up. Moreover, these ions have strong optical magnetic-dipole (M1) transitions than the previously proposed HCI clocks. They can be used for the cooling and detection techniques. To demonstrate the projected fractional uncertainties below $10^{-19}$ level, we have es…
In this article, we report on the work done with the LNE-SYRTE atomic clock ensemble during the last 10 years. We cover progress made in atomic fountains and in their application to timekeeping. We also cover the development of optical lattice clocks based on strontium and on mercury. We report on tests of fundamental physical laws made with these highly accurate atomic clocks. We also report on work relevant to a future possible redefinition of the SI second.
We identify Ba$^{4+}$ (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a $^3P_J$ fine structure manifold with anomalous energy ordering, being non-monotonic in $J$. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground ($^3P_2$) and first-excited ($^3P_0$) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a sing…
We show that optical spectroscopy of Rydberg states can provide accurate {\em in situ} thermometry at room-temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25 to 30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the Strontium clock transition. We demonstrate that magic wavelength lattices exist for both Strontium and Ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with $10^{-16}$ accuracy provide $10 \, \mathrm{mK}$ resolution and yield a blac…
The absolute frequency of the 1S0-3P0 clock transition of 87Sr has been measured to be 429 228 004 229 873.65 (37) Hz using lattice-confined atoms, where the fractional uncertainty of 8.6x10-16 represents one of the most accurate measurements of an atomic transition frequency to date. After a detailed study of systematic effects, which reduced the total systematic uncertainty of the Sr lattice clock to 1.5x10-16, the clock frequency is measured against a hydrogen maser which is simultaneously calibrated to the US primary frequency standard, the NIST Cs fountain clock, NIST-F1. The comparison i…
The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J (J=0,1,2) fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique--based on a physically motivated potential that models the presence of the ionic core--is employed to solve the Schroedinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are cal…
Quadrupole shifts for three prominent clock transitions, $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{14} 5d] ^2D_{3/2}$, $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{14} 5d] ^2D_{5/2}$ and $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{13} 6s^2] ^2F_{7/2}$, in the Yb$^+$ ion are investigated by calculating the quadrupole moments ($Θ$s) of the $5d_{3/2,5/2}$ and $4f_{7/2}$ states using the relativistic coupled-cluster (RCC) methods. We find an order difference in the $Θ$ value of the $4f_{7/2}$ state between our calculation and the experimental result, but our result concur with the other calculations that …
Fiber-based remote comparison of $^{87}$Sr lattice clocks in 24 km distant laboratories is demonstrated. The instability of the comparison reaches $5\times10^{-16}$ over an averaging time of 1000 s, which is two orders of magnitude shorter than that of conventional satellite links and is limited by the instabilities of the optical clocks. By correcting the systematic shifts that are predominated by the differential gravitational redshift, the residual fractional difference is found to be $(1.0\pm7.3)\times10^{-16}$, confirming the coincidence between the two clocks. The accurate and speedy com…
We show that three group IIIB divalent ions, B+, Al+, and In+, have anomalously small blackbody radiation (BBR) shifts of the ns^2 1S0 - nsnp 3P0 clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions, considers all relevant states in the same systematic way, and yields …
