Experimental Determination of the Landé g-Factors for 5s~2 ~1S and 5s5p ~3P States of the ~(87)Sr Atom

We present an experimental determination on the Lande g-factors for the 5 s~2 ~1 S_0 and 5 s5 p ~3 P_0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the ~(87)Sr optical lattice clock. The Zeeman shift of the 5 s5 p ~3 P_0-5 s~2 ~1 S_0 forbidden transition is measured with the π-polarized andσ~±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ~±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5 s~2 ~1 S_0 g-factor for the ~(87)Sr atom is-1.306(52) ×10~(-4), which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factorδg between the 5 s5 p~3 P_0 state and the 5 s~2 ~1 S_0 state of the ~(87)Sr atoms is measured in the experiment as well,which are-7.67(36) ×10~(-5) with π-transition spectra and-7.72(43) X 10-5 with σ~±-transition spectra, in good agreement with the previous report Phys. Rev. A 76(2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.