Lattice-induced frequency shifts in Sr optical lattice clocks at the 10(-17) level

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.     

On the bonding of small group 12 clusters

Characteristic properties as well as possible differences in bonding of small group 12 clusters M_n{\rm M}_n (M = Zn{\rm M} = {\rm Zn}, Cd, Hg; n = 2, ?, 6n = 2, \ldots, 6) have been investigated by quantum chemical ab initio methods, i.e., relativistic large-core pseudopotentials, core-polarization potentials and coupled-cluster correlation treatments. A comparison of cohesive energies and spectroscopic properties like ionization potentials, electron affinities, and vibrational frequencies reveals a close similarity between the clusters of Cd and Hg. For Zn clusters we observed an exceptional increase in stability between Zn₃\rm Zn_3 and Zn₄\rm Zn_4. In order to get a more qualitative picture of the covalent contributions to bonding we have calculated the electron localization function (ELF). The ELF analysis is in accordance with the calculated spectroscopic properties and shows predominant van der Waals interactions with weak covalent contributions for all the cluster sizes considered.     

Size dependent properties of Hgn clusters

The size dependence of ionization potentials, electron affinities and cohesive energies of small Hg _n (n= 3,4,5,6,8,13, 15) clusters has been studied using a combination of relativistic energy-consistent pseudopotentials supplemented by core-polarization potentials and highly correlated valence wavefunctions. In order to ensure a size extensive treatment of electron correlation, coupled-cluster and quantum Monte Carlo calculations have been performed, and excellent agreement observed between the results obtained with the two methods. The experimentally observed systematic trends of these properties with respect to increasing cluster size are reproduced well.     

Theoretical calculations on Landé $g$-factors and quadratic Zeeman shift coefficients of $n$s$n$p $^{3} {P}^{o}_{0}$ clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce. In this work, the hyperfine-induced Landé $g$-factors and quadratic Zeeman shift coefficients of the ${n{\rm s}n{\rm p}}$ $^3P^{\rm o}_0$ clock states for $^{111,113}$Cd and $^{25}$Mg were calculated by using the multi-configuration Dirac-Hartree-Fock theory. To obtain accurate values of these parameters, the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the Landé $g$-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy. Our calculations provide important data for estimating the first- and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.     

High-order harmonic generation in nitrogen molecules with subpicosecond visible dye-laser pulses

An experimental study of high-order harmonic generation in nitrogen molecules (N₂) has been made using intense visible (616 nm) dye-laser pulses, where the harmonic radiation up to the 21st order is observed. The harmonic distribution represents a plateau that is preceded by an intensity minimum at the 7th order. The harmonic generation characteristics were atomic-like. It has been found that there are some similarities in the high-order harmonic generation characteristics for N₂ and Ar, including the highest-order harmonics, harmonic distributions, and the influence of the multiphoton ionization on the high-order harmonic generation. These similarities are reasonably attributed to the energetic correspondence of excited levels and ionization potentials. It is pointed out that the ac Stark shift of excited levels and ionization potentials plays an important role also in the high-order harmonic generation in N₂.     

Lighting up multipolar surface plasmon polaritons by collective resonances in arrays of nanoantennas

We demonstrate the coupling of multipolar surface plasmons with photonic modes in periodic arrays of metallic nanoantennas. This coupling leads to sharp resonances known as lattice surface modes. In spite of the weak interaction of multipolar surface plasmons with light, lattice surface modes provide an efficient radiative decay channel for emitters in the proximity of the array. We observe a tenfold emission enhancement of dyes coupled to lattice resonances. Lattice surface modes light up multipolar plasmonic resonances, opening new possibilities for fluorescence spectroscopies.     

Effect of lattice strain on the Debye-Waller factors of Mg, Zn and Cd

Lattice strains in Mg, Zn and Cd powders produced by grinding have been analyzed by X-ray powder diffraction. The lattice strain (ɛ) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In all three cases viz. Mg, Zn and Cd, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Mg, Zn and Cd. The variation of energy of vacancy formation as a function of lattice strain has been studied.     

Relativistic oscillator strengths for some transitions in Cu(I), Ag(I) and Au(I)

Relativistic oscillator strengths have been calculated for transitions in the principal, sharp and diffuse series of Cu(I), Ag(I) and Au(I) spectra. The computations have been performed by employing a semiempirical method which includes exchange and core-polarization effects. A comparison is presented for the calculated ?_ik values with experimental and other theoretical data. The influence of core-polarization effects on oscillator strengths is discussed.     

锶玻色子的“魔术”波长光晶格装载实验研究

光晶格中性原子光钟的不确定度已达到10^-18量级. 本文介绍了碱土金属锶原子玻色子⁸⁸Sr在“魔术”波长处的一维光晶格装载, 实现冷锶原子的囚禁并使锶原子的钟跃迁能级(5s²) ¹S₀-(5s5p) ³P₀在此波长处的交流斯塔克光频移一致. 实验中半导体激光器产生“魔术”光波长(813 nm), 通过实验搭建光学驻波场并获得晶格激光聚焦光束, 束腰半径为38 μm. 经过一级冷却和二级冷却后温度约为2 μK的冷锶原子被此“魔术”波长光晶格囚禁. 通过实验测量得到锶原子玻色子⁸⁸Sr光晶格寿命为270 ms, 数目约为1.2×10⁵, 温度在3.5 μK左右, 此外研究了晶格光功率对晶格囚禁原子数目及温度的影响作用. 原子的光晶格装载为后续的钟跃迁提供了长的探测时间, 为进一步的光钟闭环提供了实验基础.     

锶原子光晶格钟

进入21世纪以来,锶原子光晶格钟经历了快速的发展,系统频移的不确定度指标已经超越现有的秒定义基准铯原子喷泉钟,进入到10~(-18)量级,体现了人类精密测量能力的最高水平,是精密测量物理的热点研究内容.本综述简要介绍了锶原子光晶格钟的发展水平;详细介绍了锶原子光晶格钟的各个组成部分和关键技术、如何进行精密光谱探测和闭环锁定以及各项系统频移的不确定度评估方法和锶原子跃迁绝对频率测量的方法等;最后简要介绍了锶光钟的应用和未来发展趋势.     

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.     

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.     

Role of the multipolar black-body radiation shifts in the atomic clocks at the 10−18 uncertainty level

We present here an overview of the role of the multipolar black-body radiation (BBR) shifts in the single ion atomic clocks to appraise the anticipated 10^?18 uncertainty level. With an attempt to use the advanced technologies for reducing the instrumental uncertainties at the unprecedented low, it is essential to investigate contributions from the higher-order systematics to achieve the ambitious goal of securing the most precise clock frequency standard. In this context, we have analysed contributions to the BBR shifts from the multipolar polarizabilities in a few ion clocks.     

利用钟跃迁谱线测量超稳光学参考腔的零温漂点

在87Sr光晶格钟实验系统中,通过将自由运转的698 nm激光频率锁定在由超低膨胀系数的玻璃材料构成的超稳光学参考腔上,从而获得短期频率稳定性较好的超稳窄线宽激光.超稳光学参考腔的腔长稳定性决定了最终激光频率的稳定度.为了降低腔长对温度的敏感性,使激光频率具有更好的稳定度和更小的频率漂移,利用锶原子光晶格钟的钟跃迁谱线,测量了698 nm超稳窄线宽激光系统中超稳光学参考腔的零温漂点.通过对钟跃迁谱线中心频率随温度的变化曲线进行二阶多项式拟合,得到698 nm超稳窄线宽激光系统的零温漂点为30.63℃.利用锶原子光晶格钟的闭环锁定,测得零温漂点处698 nm超稳窄线宽激光系统的线性频率漂移率为0.15 Hz/s,频率不稳定度为1.6×10^–15@3.744 s.     

KCdF3:Cr3+晶体EPR零场分裂参量与电荷补偿效应的研究

按照叠加模型与EPR零场分裂参量的三阶微扰理论,建立了KCdF₃:Cr³⁺晶体EPR零场分裂参量与四角对称Cr³⁺-Cd²⁺缺陷中心局域结构之间的定量关系.证实Cd²⁺空位与晶格畸变的存在,我们获得:围绕Cr³⁺离子的六个F^-配体分别向中心Cr³⁺移动Δ₁=0.00294nm,Δ₂=0.0010nm,Δ₃=0.0028nm (参见图2).EPR零场分裂参量与实验一致表明:Cd²⁺空位与晶格畸变的假设是合理的.尽管四角晶场主要来自Cd²⁺空位,但晶格畸变的贡献不可忽略.     

锶原子光晶格钟自旋极化谱线的探测

87Sr原子存在核自旋,在磁场作用下原子能级会分裂成不同塞曼子能级.通过光抽运对原子进行自旋极化,其自旋极化谱线的探测为锶光钟系统的闭环锁定提供精确的频率参考.本文对~(87)Sr原子钟跃迁能级5s~2~1S_0→5s5p~3P_0中的m_F=+9/2和m_F=-9/2的塞曼磁子能级自旋极化谱线进行了探测.经过一级宽带冷却和二级窄线宽冷却与俘获后,锶冷原子温度为3.9μK,原子数目为3.5×10~6.利用邻近"魔术波长"的813.426 nm半导体激光光源实现水平方向的一维光晶格装载.采用归一化探测方法用线宽为Hz量级的698 nm钟激光对~1S_0→~3P_0偶极禁戒跃迁进行探测,在150 ms的探测时间下获得线宽为6.7 Hz的钟跃迁简并谱.在磁光阱竖直方向施加一个300 mGs的偏置磁场获得塞曼分裂谱,并通过689 nm的圆偏振自旋极化光进行光抽运,最终在探测时间为150 ms时,获得左右旋极化谱线线宽分别为6.2 Hz和6.8 Hz.     

The relationship between electrical and structural characteristics of CdTe and CdMnTe layers grown on InSb

CdTe and CdMnTe layers with thickness in the range 1–2 μm have been grown by MBE on (001) InSb substrates. Measurements of the free-carrier concentration as a function of depth through these layers have revealed non-unformities attributed to the presence of extended defects arising from the relief of lattice strain resulting from the epilayer-substrate lattice mismatch. Evidence for the existence of such structural non-uniformity has been provided by DCXRD rocking curve measurements. Detailed analysis of these curves also indicates the presence of a thin interfacial layer of a different phase. The use of an excess Cd flux during growth has been found to lead to increased and more uniform carrier densities in both undoped and In doped layers.     

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).     

冷原子气体的时频测量——光晶格原子钟

基于冷原子气体的时频测量在近20年里快速发展,引起了人们的广泛关注,其典型代表是基于大量中性原子的光晶格原子钟。利用超稳钟激光同时探测囚禁在光晶格里成千上万个冷原子的钟跃迁信号,光晶格原子钟已实现10^-18量级的频率准确度和10^-17量级的秒级稳定度,大幅度提高了时频测量的精度。文章概述了光晶格原子钟的发展历史、工作原理、性能评估及应用前景。     

冷原子气体的时频测量——光晶格原子钟

基于冷原子气体的时频测量在近20年里快速发展,引起了人们的广泛关注,其典型代表是基于大量中性原子的光晶格原子钟。利用超稳钟激光同时探测囚禁在光晶格里成千上万个冷原子的钟跃迁信号,光晶格原子钟已实现10^-18量级的频率准确度和10^-17量级的秒级稳定度,大幅度提高了时频测量的精度。文章概述了光晶格原子钟的发展历史、工作原理、性能评估及应用前景。