Experimental Determination of the ${}^{24}\mathrm{Mg}$ I $(3s3p){}^{3}P_2$ Lifetime

We present the first experimental determination of the electric-dipole forbidden $(3s3p){}^{3}P_2\to (3s^2){}^{1}S_0$ ($M2$) transition rate in ${}^{24}\mathrm{Mg}$ and compare to state-of-the-art theoretical predictions. Our measurement exploits a magnetic trap isolating the sample from perturbations and a magneto-optical trap as an amplifier converting each ${}^{3}P_2\to {}^{1}S_0$ decay event into millions of photons readily detected. The transition rate is determined to be $(4.87\pm 0.3)\times {10}^{-4}{\mathrm{s}}^{-1}$ corresponding to a ${}^{3}P_2$ lifetime of ${2050}_{-110}^{+140}$ sec. This value is in agreement with recent theoretical predictions, and to our knowledge the longest lifetime ever determined in a laboratory environment.

Figure 1

Energy level diagram for ${}^{24}\mathrm{Mg}$. Atoms magnetically trapped in the ${}^{3}P_2$ state decay to the ${}^{1}S_0$ state by a magnetic quadrupole ($M2$) transition.

Figure 2

Experimental data for ${}^{3}P_2$ decay back to the ${}^{1}S_0$ ground state. Here, atoms are recaptured in the MOT and a strong fluorescence signal emerges. The red (or gray) curve is a fit of Eq. (2) to the data consistent with no intratrap collisions.

Figure 3

Raw fluorescence signal from MOT atoms after ${}^{3}P_2$ decay to ${}^{1}S_0$ (A), optical transfer (B) to the ${}^{1}S_0$ ground state, and background load of the MOT (C). The decay (A) and background signal (C) are multiplied with a factor of 100 to fit all three curves on the same plot. From the measured signal we extrapolate the signals to a time $t_{\mathrm{ref}}=500\mathrm{ms}$ for a more accurate ratio.

Figure 4

A compilation of 93 measurements of the ${}^{3}P_2$ lifetime. The red (or gray) curve is a Gaussian fit to the data. We obtain ${\Gamma }_2=(4.87\pm 0.09)\times {10}^{-4}{\mathrm{s}}^{-1}$.