Magic wavelengths for 6s_(1/2)→5d_(3/2,5/2)transitions of Yb~+ions

The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Magic Wavelengths for the 1S-2S and 1S-3S Transitions in Hydrogen Atoms

The dynamic dipole polarizabilities for 1S, 2S and 3S states of the hydrogen atom are calculated using the finite B-spline basis set method, and the magic wavelengths for 1S-2S and 1S-3S transitions are identified. In comparison of the solutions from the Schr6dinger and Dirac equations, the relativistic corrections on the magic wavelengths are of the order of 10-2 nm. The laser intensities for a 300-Er-deep optical trap and the heating rates at 514 and 1371 nm are estimated. The reliable prediction of the magic wavelengths would be helpful for the experimental design on the optical trapping of the hydrogen atoms, and in turn, it would be helpful to improve the accuracy of the measurements of the hydrogen 1S-2S and 1S-3S transitions.

Magic Wavelengths of the Optical Clock Transition at 1107 nm of Barium

Magic wavelengths for laser trapping of barium atoms in the optical clock transition at l107nm between the 6s2 1So state optical lattices are calculated with considering the and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated, Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.

Magic wavelengths for the 7s_(1/2)6d_(3/2,5/2)transitions in Ra~＋

The dynamic polarizabilities of the 7s and 6d states of Ra~＋are calculated using a relativistic core polarization potential method.The magic wavelengths of the 7s_（1/2）–6d_（3/2,5/2）transitions are identified.Comparing to the common radiofrequency（RF） ion traps,using the laser field at the magic wavelength to trap the ion could suppress the frequency uncertainty caused by the micromotion of the ion,and would not affect the transition frequency measurements.The heating rates of the ion and the powers of the laser for the ion trapping are estimated,which would benefit the possible precision measurements based on all-optical trapped Ra＋.

Magic Wavelength Measurement of the ^(87)Sr Optical Lattice Clock at NIM

We report on the magic wavelength measurement of our optical lattice clock based on fermion strontium atoms at the National Institute of Metrology （NIM）. A Ti：sapphire solid state laser locked to a reference cavity inside a temperature-stabilized vacuum chamber is employed to generate the optical lattice. The laser frequency is measured by an erbium fiber frequency comb. The trap depth is modulated by varying the lattice laser power via an acousto-optic modulator. We obtain the frequency shift coefficient at this lattice wavelength by measuring the diffbrential frequency shift of the clock transition of the strontium atoms at different trap depths, and the frequency shift coefficient at this lattice wavelength is obtained. We measure the frequency shift coefficients at different lattice frequencies around the magic wavelength and linearly fit the measurement data, and the magic wavelength is calculated to be 368554672（44）MHz.

Precision spectroscopy with a single ^(40)Ca^+ ion in a Paul trap

Precision measurement of the 4s2 S1/2-3d2 D5/2 clock transition based on 40Ca＋ ion at 729 nm is reported. A single 40Ca＋ ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly. The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5 ×10^-16. The absolute frequency of the clock transition is measured at the 10^-15 level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system （GPS）, The frequency value is 411 042 129 776 393.0（1.6） Hz with the correction of the systematic shifts. In order to carry out the comparison of two 40Ca＋ optical frequency standards, another similar 40Ca＋ optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1 × 10^-14 T-1/2 with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped 40Ca＋ ion are carried out. One is the 3d2Ds/2 state lifetime measurement, and our result of 1174（10） ms agrees well with the results reported in [Phys. Rev. A 62 032503 （2000）] and [Phys. Rev. A 71 032504 （2005）]. The other one is magic wavelengths for the 4s2S1/2-3d2Ds/2 clock transition; λ ｜mj｜=1/2= 395.7992（7） nm and λ｜m｜=3/2 = 395.7990（7） nm are reported, and it is the first time that two magic wavelengths for the 40Ca＋ clock-transition have been reported.

Calculations of the dynamic dipole polarizabilities for the Li^+ ion

The B-spline configuration-interaction method is applied to the investigations of dynamic dipole polarizabilities for the four lowest triplet states(23S,33S,23P,and 33P) of the Li+ion.The accurate energies for the triplet states of n3S,n3P,and n3D,the dipole oscillator strengths for 23S(33S)→n3P,23P(33P)→n3S,and 23P(33P)→n3D transitions,with the main quantum number n up to 10 are tabulated for references.The dynamic dipole polarizabilities for the four triplet states under a wide range of photon energy are also listed,which provide input data for analyzing the Stark shift of the Li+ion.Furthermore,the tune-out wavelengths in the range from 100 nm to 1.2 μm for the four triplet states,and the magic wavelengths in the range from 100 nm to 600 nm for the 23S→33S,23S→23P,and 23S→33P transitions are determined accurately for the experimental design of the Li+ion.

The ac Stark shifts of the terahertz clock transitions of barium

Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d3D1 and 6s5d3D2are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.