Measurement of the spin-forbidden decay rate ${\left(3s3d\right)}^1{D}_2\to \left(3s3p\right){{}^{3}P}_{2,1}$ in ${}^{24}\text{M}\text{g}$

We have measured the spin-forbidden decay rate from $\left(3s3d\right){{}^{1}D}_2\to \left(3s3p\right){{}^{3}P}_{2,1}$ in ${}^{24}\text{M}\text{g}$ atoms trapped in a magneto-optical trap. The total decay rate, summing up both exit channels $\left(3s3p\right){{}^{3}P}_1$ and $\left(3s3p\right){{}^{3}P}_2$, yields $196\pm 10{\text{s}}^{-1}$ in excellent agreement with resent relativistic many-body calculations of Porsev et al. [Phys. Rev. A 64, 012508 (2001)]. The characterization of this decay channel is important as it may limit the performance of quantum optics experiments carried out with this ladder system as well as two-photon cooling experiments currently explored in several groups.

Figure 1

Energy levels relevant for the $\left(3s3d\right){{}^{1}D}_2\to \left(3s3p\right){{}^{3}P}_{2,1}$ decay measurement in ${}^{24}\text{M}\text{g}$.

Figure 2

(Color online) (a) Experimentally the 881 nm beam is collinear with one of the MOT beams. The polarization state can be selected similar to the MOT helicity, as shown in the figure, or opposite. (b) Polarization dependent pumping of atoms in the MOT. Assuming a one-dimensional representation of the MOT the 881 nm polarization, represented by blue (dashed) line ($=\text{MOT}$ helicity) or red (solid) line, optical pumping will drive the atoms such that anisotropy in the decay rate will emerge. The green dots represents atoms trapped in the MOT quadrupole magnetic field, while red squares represent atoms in nontrapped states. The Clebsch Gordan coefficients shown will also apply to the $\left(3s3d\right){{}^{1}D}_2\to \left(3s3p\right){{}^{3}P}_1$ decay.

Figure 3

(Color online) The 881 nm laser is frequency locked to the two-photon resonance of the ladder system ${\nu }_{881}=-{\nu }_{285}=100\text{MHz}$. This ensures a maximal transfer of population to the $\left(3s3d\right){{}^{1}D}_2$. Left part of the figure shows the $\left(3s3p\right){{}^{1}P}_1$ excited state fraction obtained from the optical Bloch equations. Right part shows the experimental lock signal.

Figure 4

(Color online) Experimental values for the ratio $\frac{S^{\text{on}}}{S^{\text{off}}}$ as a function of the 881 nm Rabi frequency. (Top) Here the circular polarization corresponds to the MOT helicity [blue (dashed) lines in Fig. 2]. The curves are results from a simulations based on the optical Bloch equations, including the magnetic field of the MOT, at different decay constants $\Gamma ={\Gamma }_{22}+{\Gamma }_{21}=186$, 196, and $206{\text{s}}^{-1}$. Experiments with this circular helicity support a value of $\Gamma =196\pm 10{\text{s}}^{-1}$. (Bottom) Experiment with 881 nm polarization opposite to the MOT helicity. At a Rabi frequency of about 30 MHz the MOT is being destroyed by the destructive optical pumping effects of the 881 nm laser. Only data points below 30 MHz should be considered.