We present experimental and theoretical studies of the effect of an external magnetic field on the 3 P 0 –5 s 2 1 S 0 forbidden transition in the bosonic Sr atom. In our ultra-cold atomic system, the excitation fraction of the forbidden transition was measured under the circumstance of the different magnetic field strengths by using the normalized detection method. Based on the perturbation theory, we calculated the magnetic-field-induced 3 P 0 –5 s 2 1 S 0 transition rate as a function of the magnetic field strength. Electronic matrix elements entering the calculation of the transition rate were also used to derive the theoretical excitation fraction as a function of the magnetic field strength. A good agreement was found between the experimental measurements and the calculations. This study should be helpful in evaluating the magnetic field effects on the forbidden transition rate with higher accuracy. Moreover, it can help to understand the ultra-cold atomic interaction in the external magnetic field.
We present experimental and theoretical studies of the effect of an external magnetic field on the 3 P 0 –5 s 2 1 S 0 forbidden transition in the bosonic Sr atom. In our ultra-cold atomic system, the excitation fraction of the forbidden transition was measured under the circumstance of the different magnetic field strengths by using the normalized detection method. Based on the perturbation theory, we calculated the magnetic-field-induced 3 P 0 –5 s 2 1 S 0 transition rate as a function of the magnetic field strength. Electronic matrix elements entering the calculation of the transition rate were also used to derive the theoretical excitation fraction as a function of the magnetic field strength. A good agreement was found between the experimental measurements and the calculations. This study should be helpful in evaluating the magnetic field effects on the forbidden transition rate with higher accuracy. Moreover, it can help to understand the ultra-cold atomic interaction in the external magnetic field.
In this paper, we theoretically calculate the natural lifetime of the 5s5p3P0o state of the 87Sr atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced 5s5p3P0o−−5s21S0 clock transition rate of 87Sr is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript e refers to the excited state, i.e., the 5s5p3P0o state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the 87Sr atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.
We present an experimental determination on the Landé g-factors for the 5s 2 1 S 0 and 5 s 5 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 5s5p 3 P 0 –5s 2 1 S 0 forbidden transition is measured with the π-polarized and σ ± -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 5s 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-factor δg between the 5s5p 3 P 0 state and the 5s 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) × 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 .
Quantum-mechanical interference is found in the two-photon excitation of an atomic 1S through the nonresonant sequence 11P\ensuremath{\leftarrow}1S, since the magnetic sublevels of the intermediate 1P state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s)1S\ensuremath{\leftarrow}(5s2)1S transition of atomic Sr excited by two dye lasers operating at different wavelengths.
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
A method for quantum-mechanical calculations of cross sections for the Zeeman transitions in collisions of 3P atoms with structureless targets in a magnetic field is presented and applied to the study of magnetic and electronic relaxation in oxygen-helium and carbon-helium collisions at cold and ultracold temperatures. The rate constants for collisionally induced transitions between Zeeman levels in ground-state oxygen have large magnitudes in a 1 T field. It is shown that magnetic fields induce the forbidden 3P1 $\ensuremath{\rightarrow}$ 3P0 transition in ultracold collisions of carbon with helium. The cross section vanishes at zero energy for field-free collisions, but becomes infinitely large in a finite magnetic field, varying with velocity v and magnetic field B as B2/v.
The Measurement of Landé g Factor of 3D1 with Cold 88Sr Atoms
We experimentally observed the resolved Zeeman spectroscopy of the3P0-3D1 transition using the cold88Sr atoms, and measured the Landé g factor of3D1on the basis of the observable spectroscopy under different magnetic fields, which indicates the measured value is 0.4997(91) in good agreement with the calculated value of 0.4988. The detailed experimental scheme is presented here. Benefitting from the scheme, Sr atoms can be trapped in a mageto-optical trap (MOT) at a low temperature and a high density. The measurement of gJof3D1is beneficial to investigate the long range dipolar interaction on the3P0-3D1 transition of88Sr.