Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) 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 Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) 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 Landég-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.

A transportable optical lattice clock at the National Time Service Center

We report a transportable one-dimensional optical lattice clock based on 87Sr at the National Time Service Center.The transportable apparatus consists of a compact vacuum system and compact optical subsystems.The vacuum system with a size of 90 cm×20 cm×42 cm and the beam distributors are assembled on a double-layer optical breadboard.The modularized optical subsystems are integrated on independent optical breadboards.By using a 230 ms clock laser pulse,spin-polarized spectroscopy with a linewidth of 4.8 Hz is obtained which is close to the 3.9 Hz Fourier-limit linewidth.The time interleaved self-comparison frequency instability is determined to be 6.3 × 10^-17 at an averaging time of 2000 s.

First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM

An optical lattice clock based on 87Sr is built at National Institute of Metrology （NIM） of China. The systematic frequency shifts of the clock are evaluated with a total uncertainty of 2.3×10-16. To measure its absolute frequency with respect to NIM＇s cesium fountain clock NIM5, the frequency of a flywheel H-maser of NIM5 is transferred to the Sr laboratory through a 50-kin-long fiber. reference frequency of this H-maser, is used for the optical this Sr clock is measured to be 429228004229873.7（1.4）Hz. A fiber optical frequency comb, phase-locked to the frequency measurement. The absolute frequency of

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.

Interrogation of optical Ramsey spectrum and stability study of an ^(87)Sr optical lattice clock

The optical Ramsey spectrum is experimentally realized in an ^(87)Sr optical lattice clock, and the measured linewidth agrees well with theoretical expectation. The coherence time between the clock laser and the atoms, which indicates the maximum free evolution period of using Ramsey detection to measure the atom-laser phase information, is determined as 340(23) ms by measuring the fringe contrasts of the Ramsey spectrum as a function of the free evolution period. Furthermore, with the same clock duty cycle of about 0.1, the clock stability is measured by using the Ramsey and Rabi spectra,respectively. The experimental and theoretical results show approximately the same stability as the two detection methods, which indicates that Ramsey detection cannot obviously improve the clock stability until the clock duty cycle is large enough. Thus, it is of great significance to choose the detection method of a specific clock.

A Longitudinal Zeeman Slower Based on Ring-Shaped Permanent Magnets for a Strontium Optical Lattice Clock

We report a longitudinal Zeeman slower based on ring-shaped permanent magnetic dipoles used for the strontium optical lattice clock. The Zeeman slower is composed of 40 permanent magnets with the same outer diameter but different inner diameters. The maximum variation of the axial field from its target values is less than 2%. In most parts of the Zeeman slower, the intensity variations of the field in radial spatial distribution are less than 0.1 roT. With this Zeeman slower, the strontium atoms are slowed down to 95m/s, and approximately 2% of the total atoms are slowed down to less than 50m/s.

Theoretical calculation of the quadratic Zeeman shift coefficient of the^(3)P_(0)^(o)clock state for strontium optical lattice clock

In the weak-magnetic-field approximation,we derived an expression of quadratic Zeeman shift coefficient of^(3)P_(0)^(o)clock state for^(88)Sr and^(87)Sr atoms.By using this formula and the multi-configuration Dirac-Hartree-Fock theory,the quadratic Zeeman shift coefficients were calculated.The calculated values C_(2)=-23.38(5)MHz/T^(2) for^(88)Sr and the^(3)p_(0)^(o),F=9/2,M_(F)=±9/2 clock states for^(87)Sr agree well with the other available theoretical and experimental values,especially the most accurate measurement recently.In addition,the calculated values of the^(3)p_(0)^(o),F=9/2,M_(F)=±9/2 clock states were also determined in our^(87)Sr optical lattice clock.The consistency with measurements verifies the validation of our calculation model.Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition,for example,the new proposed^(1)S_(0),F=9/2,M_(F)=±5/2-^(3)P_(0)^(o),F=9/2,M_(F)=±3/2 transitions.

A proposal for detecting weak electromagnetic waves around 2.6μm wavelength with Sr optical clock

Infrared signal detection is widely used in many fields.Due to the detection principle,however,the accuracy and range of detection are limited.Thanks to the ultra stability of the^(87)Sr optical lattice clock,external infrared electromagnetic wave disturbances can be responded to.Utilizing the ac Stark shift of the clock transition,we propose a new method to detect infrared signals.According to our calculations,the theoretical detection accuracy in the vicinity of its resonance band of 2.6μm can reach the order of 10-14W,while the minimum detectable signal of common detectors is on the order of 10^(-10)W.

Clock-transition spectrum of ^(171)Yb atoms in a one-dimensional optical lattice

An optical atomic clock with 171yb atoms is devised and tested. By using a two-stage Doppler cooling technique, the 171Yb atoms are cooled down to a temperature of 6 ± 3 μK, which is close to the Doppler limit. Then, the cold 171Yb atoms are loaded into a one-dimensional optical lattice with a wavelength of 759 nm in the Lamb-Dicke regime. Furthermore, these cold 171yb atoms are excited from the ground-state 1S0 to the excited-state 3P0 by a clock laser with a wavelength of 578 nm. Finally, the 1S0-3P0 clock-transition spectrum of these 171yb atoms is obtained by measuring the dependence of the population of the ground-state 1 S0 upon the clock-laser detuning.

Precise measurement of 171Yb magnetic constants for 1S_(0)–3P_(0) clock transition

We present a precise measurement of171Yb magnetic constants for 1S_(0)-3P_(0) clock transition. The background magnetic field is firstly compensated to < 1 m Gs(1 Gs = 10^(-4)T) through measuring the splitting of two π transitins of171Yb clock transition at different compensation coils currents. Then, the splitting ratios of the π and σ components of171Yb clock transition at different bias magnetic fields are measured, and the first-order Zeeman coefficient is determined to beα = 199.49(5) Hz/Gs. The second-order Zeeman shifts at various bias magnetic fields are also measured through interleaved self-comparison in which the bias magnetic fields are modulated between high and low values. The second-order Zeeman coefficient is fitted to be β =-6.09(3) Hz/m T^(2), which is consistent with the result of NIST group.