高准确度的钙离子光频标

近年来,冷原子技术和激光技术促进了高精度光频标的发展,有望在建立时间基准、推动基础研究和满足国家需求等方面发挥重要的作用.本文介绍了中国科学院武汉物理与数学研究所近年来在高准确度钙离子(~(40)Ca~+)光频标研究方面的进展:采用新的ULE腔系统,实现了729 nm钟跃迁激光器1—100 s的频率稳定度均优于2×10~(-15),通过对外场和环境效应的控制及克服,特别是囚禁离子运动效应的抑制,获得单个钙离子光频标的不确定度优于5.5×10~(-17);通过两台光频标的比对,测得20000 s的稳定度也进入10~(-17)量级;基于高精度钙离子光频标平台,进行了相关精密测量的工作,包括:基于全球定位系统的超高精度远程光频绝对值测量方案,第二次测量了钙离子的光频跃迁绝对值,该测量结果再次被国际时间频率咨询委员会采纳,更新了钙离子的频率推荐值;精确测量了钙离子的钟跃迁魔幻波长,由此提出新型的全光囚禁离子光频标的方法;精密测量了钙离子的亚稳态寿命等参数.以上工作推动了基于冷原子的精密测量工作.     

飞秒光梳和碘稳频532nm Nd:YAG激光频率的测量

报道了中国计量科学研究院研制的基于掺钛蓝宝石(Ti:Sapphire)锁模飞秒脉冲激光器的飞秒光学频率梳装置，并利用此装置测量了碘稳频532nm(¹²⁷I₂R(56)32-10) Nd∶YAG固体激光器的频率，结果为 563260223512991±20Hz,相对不确定度为3.6×10^-14.这一数值是直接溯源到铯原子微波频率基准的光学频率测量结果.     

Subhertz-linewidth infrared frequency source with a long-term instability below 5 × 10−15

Distributing a stable, absolute optical reference frequency via fiber network would serve research and development in academia and industry. Lasers stabilized to high-finesse Fabry–Pérot cavities can achieve fractional frequency instabilities of less than 10^?15 for periods up to several seconds. Their instabilities increase for longer averaging times due to a variable frequency drift, with a linear drift component of the order of 10…100 mHz/s. Hydrogen masers, on the other hand, yield an instability floor of a few parts in 10^?15, but suffer from poor stabilities on short timescales. We demonstrate an infrared optical frequency source that combines a cavity-stabilized laser with a hydrogen maser to achieve a residual fractional frequency instability better than 5 × 10^?15 for all averaging times from 0.4 up to 10,000 s. The frequency drift of the system over a period of 40,000 s is less than 30 µHz/s. For obtaining absolute frequency accuracy, the hydrogen maser is referenced to a primary frequency standard.     

The transportable cesium fountain clock NIM5: its construction and performance

The second laser cooling cesium fountain clock NIM5 at the National Institute of Metrology (NIM) China adopts the (1,1,1) direct optical molasses ( OM) configuration. NIM5 has been running with a stability of 3×10⁻¹⁵/d and an operation ratio of 99% since 2007. Preliminary evaluations of NIM5 in 2008 showed a typical combined uncertainty of 3×10⁻¹⁵. The NIM5 clock is operating in parallel with NIM’s first fountain clock NIM4. NIM4 and NIM5 are used to steer the frequency of the calculated NIM atomic time TA-c(NIM) and the first set of results are promising. We are now at the stage of comparing the frequency of NIM5 with UTC to support the independent frequency shift evaluations of NIM5 and contribute to the international atomic time in the near future.      

Linear Paul trap design for an optical clock with Coulomb crystals

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 the ions at a level at which the corresponding second-order Doppler shift contributes less than 10^?18 to the relative uncertainty of the frequency standard.     

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001(2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10.5 a.u.. The scalar and tensor polarizabilities(α0, α2) and hyperpolarizabilities(γ0, γ2, γ4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities,which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.     

Preliminary frequency measurement of the electric quadrupole transition in a single laser-cooled 40Ca+ ion

The trapping and laser cooling of ⁴⁰Ca⁺ ion on the way toward optical frequency standards have been developed. A single ⁴⁰Ca⁺ ion is trapped in the miniature Paul trap and laser cooled by two frequency-stabilized diode lasers. A commercial Ti:Sapphire laser system at 729 nm is referenced to a high-finesse cavity to meet the requirements of ultra narrow linewidth of the 4s²S_1/2-3d²D_5/2 electric quadrupole transition. Its center frequency is preliminarily measured to be 411 042 129 686.1 (2.6) kHz. The attempt to finally lock the 729-nm laser system to atomic transition is made. Further work to improve the accuracy of measurement and the stabilization of system locking is in consideration and preparation.     

Improvements and New Evaluation of NIM4 Caesium Fountain Clock at NIM in 2005-2006

The NIM4 caesium fountain clock has been operating stably and sub-continually since August 2003. We present our improvements on NIM4 in 2005-06 and the most recent evaluation for its frequency shifts with an uncertainty of 5 × 10^-15. A 203-day comparison between NIM4 and GPS time shows an agreement of 2 × 10^-14. Finally the construction of the NIM5 transportable caesium fountain clock is briefly reported.     

Preliminary frequency measurement of the electric quadrupole transition in a single laser-cooled 40Ca+ ion

The trapping and laser cooling of ⁴⁰Ca⁺ ion on the way toward optical frequency standards have been developed. A single ⁴⁰Ca⁺ ion is trapped in the miniature Paul trap and laser cooled by two frequency-stabilized diode lasers. A commercial Ti:Sapphire laser system at 729 nm is referenced to a high-finesse cavity to meet the requirements of ultra narrow linewidth of the 4s²S_1/2-3d²D_5/2 electric quadrupole transition. Its center frequency is preliminarily measured to be 411 042 129 686.1 (2.6) kHz. The attempt to finally lock the 729-nm laser system to atomic transition is made. Further work to improve the accuracy of measurement and the stabilization of system locking is in consideration and preparation.      

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.     

Improved absolute frequency measurement of the 115In+ 5s2 1S0-5s5p3P0 narrowline transition: Progress towards an optical frequency standard

We report on an improved absolute frequency measurement of the 5s ^{2 1} S ₀0-5s5p ³ P ₀ narrowline clock transition at 236.5 nm, for a single, trapped, and laser-cooled ¹¹⁵In ion. Using a narrowline laser as the local oscillator, a linewidth of 43 Hz for the transition is resolved. The uncertainty of the transition frequency’s centroid is 18 Hz, leading to a fractional uncertainty of 1.4 × 10⁻¹⁴. For absolute frequency measurement, we use an optical frequency comb locked to a cesium clock as the reference. The transition frequency is found to be 1267402452900967(63) Hz, averaged over 13 days of separate measurements. The accuracy is about 5.0 × 10⁻¹⁴. We discuss possibilities for further improvement. Original Text ? Astro, Ltd., 2007.     

A diode laser spectrometer at 634nm and absolute frequency measurements using optical frequency comb

This paper reports that two identical external-cavity-diode-laser (ECDL) based spectrometers are constructed at 634 nm referencing on the hyperfine B-X transition R(80)8-4 of ¹²⁷I₂. The lasers are stabilized on the Doppler-free absorption signals using the third-harmonic detection technique. The instability of the stabilized laser is measured to be 2.8×10^-12 (after 1000 s) by counting the beat note between the two lasers. The absolute optical frequency of the transition is, for the first time, determined to be 472851936189.5 kHz by using an optical frequency comb referenced on the microwave caesium atomic clock. The uncertainty of the measurement is less than 4.9 kHz.     

Ra+ ion trapping: toward an atomic parity violation measurement and an optical clock

A single Ra⁺ ion stored in a Paul radio frequency ion trap has excellent potential for a precision measurement of the electroweak mixing angle at low momentum transfer and as the most stable optical clock. The effective transport and cooling of singly charged ions of the isotopes ²⁰⁹Ra to ²¹⁴Ra in a gas filled radio frequency quadrupole device is reported. The absolute frequencies of the transition 7s²S_1/2–7d²D_3/2 at wavelength 828 nm have been determined in ^212–214Ra⁺ with ≤19 MHz uncertainty using laser spectroscopy on small samples of ions trapped in a linear Paul trap at the online facility Trapped Radioactive Isotopes: µicrolaboratories for fundamental Physics (TRIµP) of the Kernfysisch Versneller Instituut.     

A high-precision segmented Paul trap with minimized micromotion for an optical multiple-ion clock

We present a new setup to sympathetically cool ¹¹⁵In⁺ ions with ¹⁷²Yb⁺ for optical clock spectroscopy. A first prototype ion trap made of glass-reinforced thermoset laminates was built, based on a design that minimizes axial micromotion and offers full control of the ion dynamics in all three dimensions. We detail the trap manufacturing process and the characterization of micromotion in this trap. A calibration of the photon-correlation spectroscopy technique demonstrates a resolution of 1.1 nm in motional amplitude of our measurements. With this method, we demonstrate a sensitivity to systematic clock shifts due to excess micromotion of $|(\Updelta\nu/\nu)_{\rm mm}|=7.7\times10^{-20}$ along the direction of the spectroscopy laser beam. Owing to our on-board filter electronics on the ion trap chips, no rf phase shifts could be resolved at this level. We measured rf fields over a range of 400 μm along the ion trap axis and demonstrated a region of 70 μm where an optical frequency standard with a fractional inaccuracy of ≤1 × 10^?18 due to micromotion can be operated.     

基于飞秒光频梳的双频He-Ne激光器频率测量

利用光纤飞秒光频梳和外腔可调谐半导体激光器, 建立了一套双频He-Ne激光器频率测量系统. 选用铷钟作为系统的频率基准, 通过将外腔半导体激光锁定至光频梳使得其频率溯源至铷钟, 再利用外腔可调谐半导体激光与双频He-Ne激光器输出的正交偏振激光拍频, 同时测量两路正交偏振激光频率. 将可调谐半导体激光器锁定至光频梳第1894449个梳齿, 其绝对频率为473612190000.0±2.7 kHz, 相对不确定度为5.7×10^-12. 对商品双频He-Ne激光器进行频率测量实验, 双频He-Ne激光器水平方向偏振激光频率均值为473612229934 kHz, 竖直方向偏振激光频率均值为473612232111 kHz, 平均时间为1024 s的相对Allan标准差为5.2×10^-11, 频差均值为2.177 MHz, 标准偏差为2 kHz.     

Electric quadrupole shift cancellation in single-ion optical frequency standards

The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for cancelling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of 5 x 10(-18) for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the 5s (2)S(1/2)-4d (2)D(5/2) clock transition of 88Sr+.     

Synthesis of two-species ion chains for a new optical frequency standard with an indium ion

Ion chains consisting of different species play an important role in new applications in quantum information processing as well as in optical frequency standards. We demonstrate generation and stabilization of ion chains consisting of Ca⁺ and In⁺. The Ca⁺ chains with In⁺ located at specified positions are synthesized using resonant photo-ionization, real-time imaging and trap field control techniques. A specific configuration of an ion chain is stabilized by destabilizing other configurations via selective excitation of vibrational modes using amplitude modulation on the cooling laser beam. New approaches to an indium ion optical clock are proposed using the ions chains.     

Hydrogen maser frequency shifts due to coherently excited Δm F =±1 transitions betweenF=1 levels of the atomic hydrogen ground state

Hydrogen maser frequency shifts, caused by the multiple quantum transition nonlinearities of a resonant multiple frequency excitation of the atomic hydrogen four level ground state system have been investigated. The oscillation characteristics of hydrogen maser operation with simultaneously excited, low frequencyΔm _F =±1 transitions between theF=1 states of the atomic hydrogen ground state have been analysed theoretically and explicit formulas for hydrogen maser frequency shifts and amplitude response have been derived for arbitrary maser oscillation amplitude and a small signal approximation for theΔm _F =±1 “Zeeman” transitions. The comparison with experimentally observed hydrogen maser frequency shifts was specialized to small magnetic fields, for which the difference between the resonance frequencies of the two low frequency,Δm _F =±1 Zeeman transitions is small compared to the linewidth. Special emphasis was placed on the evaluation of frequency pulling effects for a Zeeman transition excitation at off-resonance conditions. For this case the theoretical formulation of frequency pulling effects becomes insensitive against simplifying assumptions about the radiation damping phenomena and a particular good agreement between experiment and theory can therefore be expected. Experimental conditions have been specified, for which the uncertainty of hydrogen maser frequency due to Zeeman transition induced frequency shifts does not restrict the present frequency stability of a hydrogen maser frequency standard.     

Long range interactions of the Mg+ and Ca+ ions

The polarizabilities of the low lying states of the Mg⁺ and Ca⁺ ions are evaluated by diagonalizing the semi-empirical Hamiltonians in a large dimension single electron basis. The quadrupole moment of the metastable 3d state Ca⁺ is also calculated and is within 1% of a recent experimental value while being 5% smaller than some large ab-initio calculations. In addition, the long range dispersion coefficients for these ions interacting with a number of atoms are given. Oscillator strengths are also given and generally agree with the most sophisticated ab-initio calculations. The polarizabilities and dispersion coefficients can be used to estimate the frequency shifts of the Ca⁺ 4s ↦ 3d clock transition due to background electric fields and also collisions with a buffer gas.