Measurement of the (199)Hg+ 5d9 6s2 (2)D(5/2) electric quadrupole moment and a constraint on the quadrupole shift

The electric-quadrupole moment of the (199)Hg+ 5d9 6s2 (2)D(5/2) state is measured to be theta(D,5/2) = -2.29(8) x 10(-40) C m2. This value was determined by measuring the frequency of the (199)Hg+ 5d10 6s (2)S(1/2) --> 5d9 6s2 (2)D(5/2) optical clock transition for different applied electric-field gradients. An isolated, mechanically stable optical cavity provides a frequency reference for the measurement. We compare the results with theoretical calculations and discuss the implications for the accuracy of an atomic clock based upon this transition. We now expect that the frequency shift caused by the interaction of the quadrupole moment with stray electric-field gradients will not limit the accuracy of the Hg+ optical clock at the 10(-18) level.     

可搬运锶光晶格钟系统不确定度的评估

可搬运光学原子钟在科学研究和工程应用中具有重要意义.本文测量了可搬运87Sr光晶格钟系统的主要频移,包括黑体辐射频移、碰撞频移、晶格光交流斯塔克频移、二阶塞曼频移等.首先实验上测量了磁光阱腔体表面的温度分布,分析了不同热源对原子团的影响,得到黑体辐射总的相对频移修正量为50.4×10^-16.相对不确定度为5.1×10^-17.然后利用分时自比对方法,评估了碰撞频移、晶格光交流斯塔克频移和二阶塞曼频移.结果表明,由黑体辐射引起的频移量最大,晶格光交流斯塔克频移的不确定度最大,系统总的相对频移修正量为58.8×10^-16,总不确定度为2.3×10^-16.该工作为可搬运87Sr光晶格钟之后的性能提升和应用提供了条件.     

Hg~+离子5d~(10)6s ~2S_(1/2)→5d~96s~2 ~2D_(5/2)钟跃迁同位素位移和超精细结构的理论研究

本文首先在Dirac-Hartree-Fock近似下理论评估了Hg~+离子5d~(10)6s ~2S_(1/2)→5d~96s~2 ~2D_(5/2)钟跃迁的质量位移(mass shift, MS)和场位移(field shift, FS)在其同位素位移(isotope shift, IS)中的相对贡献,发现MS远小于FS而可以被忽略.在此基础上,通过系统地考虑该原子体系中主要的电子关联效应,计算了这条钟跃迁FS的精确值以及涉及到的上下两个能级的超精细结构常数,并得到了几种稳定汞同位素离子该跃迁的IS和超精细结构分裂.其中,计算的~(199)Hg~+和~(198)Hg~+离子之间的钟跃迁频率偏移与已有实验测量值相比误差为2%左右.最终,本文给出了汞离子7种常见同位素该谱线的绝对频率值,为实验上的谱线测量提供了有效的理论依据.     

Accuracy evaluation of an optical lattice clock with bosonic atoms

We report what we believe to be the first accuracy evaluation of an optical lattice clock based on the S01-->P03 transition of an alkaline earth boson, namely, Sr88 atoms. This transition has been enabled by using a static coupling magnetic field. The clock frequency is determined to be 429228066418009(32)Hz. The isotopic shift between Sr87 and Sr88 is 62188135Hz with fractional uncertainty 5x10(-7). We discuss the necessary conditions to reach a clock accuracy of 10(-17) or less by using this scheme.     

Measurement of the absolute energy level and hyperfine structure of the 87Rb 4D5/2 state

We have measured the absolute frequency of the excited state transition 5P(3/2)-4D(5/2) in a (87)Rb atom with a femtosecond frequency comb, utilizing the recently developed spectroscopic technique of the double resonance optical pumping method. The absolute energy level of the 4D(5/2) state is determined by measuring the absolute frequency of the 5S(1/2)-5P(3/2) transition simultaneously. The hyperfine structure constants of the 4D(5/2) state are obtained by using the measured frequency. The magnetic dipole constant, A, is determined to be (-16.747+/-0.010) MHz with an uncertainty reduced 60-fold compared with a previous result. The electric quadrupole constant, B, is determined, for what is to our knowledge the first time, to be (4.149+/-0.059) MHz.     

Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+

The quadrupole moment of the 4d (2)D(5/2) level in 88Sr+ has been measured to be 2.6(3)ea(2)(0), where a(0) is the Bohr radius and e the elementary charge. A single laser-cooled strontium ion was confined in an end cap trap with a variable dc quadrupole potential, and measurements were made on the 5s (2)S(1/2)-4d (2)D(5/2) transition at 674 nm using a femtosecond optical frequency comb. This work shows that measurements of the unperturbed 88Sr+ transition frequency with sub-Hz uncertainty are possible and is important in understanding the reproducibility of ion trap optical frequency standards.     

Optical lattice induced light shifts in an yb atomic clock

We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).     

Magnetic field measurement based on a stimulated two-photon Raman transition

The magnetic field in the microwave interaction zone of the fountain atomic clock was measured by stimulated Raman transitions.By measuring the two-photon transition frequency between the Zeeman levels of the two ground states,we achieved a magnetic field measurement accuracy of the order of 0.28 nT.This method is immune to the Doppler shift and the AC Stark shift.The second order Zeeman shift of the fountain clock is 170.7×10-15,with the uncertainty of 7.2×10-16.     

Absolute frequency measurement and high resolution spectroscopy of In 5sS0-5s5p P0 narrowline transition

We measure the frequency of the 5s²¹S₀-5s5p ³P₀ narrowline clock transition at 236.5 nm, for a single, trapped and laser cooled ¹¹⁵In⁺ ion. In the experiment, an ultra-narrow linewidth laser (<1.34 Hz at 3 s integration time) is used to interrogate the clock transition for high resolution spectroscopy. A linewidth of 43 Hz of the clock transition is observed. The uncertainty of the line centroid is 18 Hz, leading to a fractional uncertainty of 1.4×10^-14. The frequency is measured by using an optical frequency comb referenced to a cesium clock. The transition frequency is found to be 1, 267, 402, 452, 901.265 (256) kHz, averaged over 13 days of separate measurement. The accuracy of 2.35×10^-13 is due to the reference cesium clock calibrated against UTC time. We discuss ways for further improvements.     

Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb

With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of 2x10(-13) in 5 s , to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the Hg(+) clock transition with an improvement in accuracy of ~10(5) compared with its best previous measurement.     

Evaluation of second-order Zeeman frequency shift in NTSC-F2

Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition|F = 3, mF=-1 → |F = 4, mF=-1 central frequency, obtaining this frequency shift as 131.03×10~(-15) and constructing the C-field profile(σ = 0.15 n T). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition |F = 3, mF=-1 → |F = 4, mF=-1 fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10×10~(-15). The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6×10~(-17). Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.     

Single-ion nuclear clock for metrology at the 19th decimal place

The 7.6(5) eV nuclear magnetic-dipole transition in a single 229Th3+ ion may provide the foundation for an optical clock of superb accuracy. A virtual clock transition composed of stretched states within the 5F(5/2) electronic ground level of both nuclear ground and isomeric manifolds is proposed. It is shown to offer unprecedented systematic shift suppression, allowing for clock performance with a total fractional inaccuracy approaching 1×10(-19).     

87Sr lattice clock with inaccuracy below 10 -15

Aided by ultrahigh resolution spectroscopy, the overall systematic uncertainty of the 1S0-3P0 clock resonance for lattice-confined 87Sr has been characterized to 9 x 10(-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 x 10(-15) fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency to date.     

利用传输腔技术实现镱原子光钟光晶格场的频率稳定

为了获得高稳定度和高精确度的原子光晶格钟,光晶格场的频率必须得到锁定,线宽必须控制到特定水平用来消除交流斯塔克频移.本文提出利用传输腔技术来实现对镱原子光钟的光晶格场的频率锁定和抑制频率长期漂移的锁定方案.首先,将一个殷钢材料的传输腔锁定在基于调制转移谱技术锁定的780 nm激光场上,再将759 nm的光晶格光场锁定在传输腔上.实验结果表明,光晶格光场的线宽可以锁定和控制在1 MHz以下.光晶格光场与锁定于氢钟的光梳拍频结果显示,光晶格光场的长期频率稳定度优于3.6×10~(-10),可以确保实现镱原子光钟的不确定度进入10~(-17).     

Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock

We measure a cold collision frequency shift in an 87Rb fountain clock that is fractionally 30 times smaller than that for Cs. The shift is -0.38(8) mHz for a density of 1.0(6)x10(9) cm(-3). We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding 2(lambda(10)-lambda(20))/(lambda(10)+lambda(20)) = 0.1(6).     

High-accuracy optical clock based on the octupole transition in 171Yb+

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.     

Improvement of the fractional uncertainty of a neutral-atom calcium optical frequency standard to 2×10-14

We have investigated the two major effects that limit the accuracy of an optical frequency standard based on laser-cooled neutral calcium atoms, i.e. the residual Doppler shift and atomic collisions. A new correction method was applied to reduce the contribution of the residual Doppler effect to the total fractional uncertainty to 1×10^-14. Measurements of the shift of the clock transition frequency due to cold collisions allowed us to reduce their contribution to 4×10^-15. With these improvements we have reduced the total fractional frequency uncertainty of the standard by nearly an order of magnitude to 2×10^-14. Received: 9 August 2002 / Revised version: 16 November 2002 / Published online: 26 February 2003 RID="*" ID="*"Permanent address: Russian Academy of Sciences, P.N. Lebedev Physical Institute, Samara Branch, Novo-Sadovaya st. 221, Samara 443011, Russia RID="**" ID="**"Corresponding author. Fax: +49-531/592-4305, E-mail: uwe.sterr@ptb.de     

Absolute frequency measurement of the In+ clock transition with a mode-locked laser

The absolute frequency of the In(+) 5s(2) (1)S(0)5s5p (3)P(0) clock transition at 237 nm was measured with an accuracy of 1.8 parts in 10(13). Using a phase-coherent frequency chain, we compared the (1)S(0)(3)P(0) transition with a methane-stabilized HeNe laser at 3.39 mum, which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the HeNe standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In(+) clock transition was found to be 1 267 402 452 899.92 (0.23) kHz, the accuracy being limited by the uncertainty of the HeNe laser reference. This result represents an improvement in accuracy of more than 2 orders of magnitude over previous measurements of the line and now stands as what is to our knowledge the most accurate measurement of an optical transition in a single ion.s.     

Precision calculation of blackbody radiation shifts for optical frequency metrology

We show that three group IIIB divalent ions, B(+), Al(+), and In(+), have anomalously small blackbody radiation (BBR) shifts of the ns(2) (1)S(0)-nsnp (3)P(0)(o) 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 and yields a rigorous upper bound on the uncertainty of the final results. We reduce the BBR contribution to the fractional frequency uncertainty of the Al(+) clock to 4×10(-19) at T=300 K. We also reduce the uncertainties due to this effect at room temperature to 10(-18) level for B(+) and In(+) to facilitate further development of these systems for metrology and quantum sensing.