Two-photon cooling of magnesium atoms

A two-photon mechanism for cooling atoms below the Doppler temperature is analyzed. We consider the magnesium ladder system $\left(3s^2\right){}^{1}S_0\to \left(3s3p\right){}^{1}P_1$ at $285.2\mathrm{nm}$ followed by the $\left(3s3p\right){}^{1}P_1\to \left(3s3d\right){}^{1}D_2$ transition at $880.7\mathrm{nm}$. For the ladder system quantum coherence effects may become important. Combined with the basic two-level Doppler cooling process this allows for reduction of the atomic sample temperature by more than a factor of 10 over a broad frequency range. First experimental evidence for the two-photon cooling process is presented and compared to model calculations. Agreement between theory and experiment is excellent. In addition, by properly choosing the Rabi frequencies of the two optical transitions a velocity independent atomic dark state is observed.

Figure 1

Energy levels relevant for the two-photon transition $\left(3s^2\right){}^{1}S_0\to \left(3s3p\right){}^{1}P_1\to \left(3s3d\right){}^{1}D_2$ in ${}^{24}\mathrm{Mg}$.

Figure 2

(Color online) Calculated temperature $T$ relative to the ∣0⟩–∣1⟩ Doppler temperature $T_D$ as a function of ir detuning. The uv detuning is ${\delta }_1=-100\mathrm{MHz}$ and the Rabi frequencies ${\Omega }_1=40\mathrm{MHz}$ and ${\Omega }_2=120\mathrm{MHz}$, respectively.

Figure 3

Energy eigenvalues and decay rates obtained from diagonalizing Eq. (5) for ${\delta }_1=-100\mathrm{MHz}$, ${\Omega }_1=40\mathrm{MHz}$, and ${\Omega }_2=600\mathrm{MHz}$. These values correspond to the experiment decribed below. The dark state (solid line) is present for a ir frequency detuning of about $0–600\mathrm{MHz}$.

Figure 4

Images of the MOT without the horizontal ir beam and with the horizontal ir beam, at ${\Omega }_1=40\mathrm{MHz}$ and ${\Omega }_2=600\mathrm{MHz}$. The ir beam size of $200\mu \mathrm{m}$ is reproduced in the right image, the bright tunnel through the image (bright color means less fluorescence). The laser detunings were ${\delta }_1=-100\mathrm{MHz}$ and ${\delta }_2=400\mathrm{MHz}$.

Figure 5

(Color online) Experimental data for the MOT radius compared with the theoretical prediction presented in Fig. 2. The radius is related to the temperature by using the equipartition theorem. No fitting parameters are introduced, merely experimental determined values of ${\delta }_1=-100\mathrm{MHz}$ and Rabi frequencies of ${\Omega }_1=40\mathrm{MHz}$, ${\Omega }_2=120\mathrm{MHz}$, respectively.