Efficient repumping of a Ca magneto-optical trap

We investigate the limiting factors in the standard implementation of the Ca magneto-optical trap. We find that intercombination transitions from the $4s5p{}^1{P}_1$ state used to repump the electronic population from the $3d4s{}^1{D}_2$ state severely reduce the trap lifetime. We explore seven alternative repumping schemes theoretically and investigate five of them experimentally. We find that all five of these schemes yield a significant increase in the trap lifetime and consequently improve the number of atoms and peak atom density by as much as $\sim 20$ times and $\sim 6$ times, respectively. One of these transitions, at 453 nm, is shown to approach the fundamental limit for a Ca magneto-optical trap with repumping only from the dark $3d4s{}^1{D}_2$ state, yielding a trap lifetime of $\sim 5$ s.

Figure 1

Comparison of the calculated CI + MBPT transition rates with 111 available experimental data. Transitions involving a state with orbital angular momentum $l\ge 3$ or principal quantum number $n\ge 6$ are shown in blue. All other transitions are shown in black. Error bars correspond to the experimental error.

Figure 2

Relevant level structure for operation of a standard calcium MOT. Laser cooling is accomplished on the 423-nm $4s4p{}^1{P}_1\leftarrow 4s^2{}^1{S}_0$ transition. Atoms that decay to the $3d4s{}^1{D}_2$ state are repumped back into the cooling cycle via the 672-nm $4s5p{}^1{P}_1\leftarrow 3d4s{}^1{D}_2$ transition, while those in the long-lived $4s4p{}^3{P}_{0,2}$ states are lost from the MOT.

Figure 3

Simplified calcium electronic level structure showing the eight repumping transitions considered here. All transitions except those at 504 and 535 nm have been studied experimentally. The overall best Ca MOT performance is found when pumping to a highly configuration-mixed state, labeled $4snp{}^1{P}_1$, using the 453-nm $4snp{}^1{P}_1\leftarrow 3d4s{}^1{D}_2$ transition.

Figure 4

Measured calcium MOT density as a function of the repumping laser detuning for (a) the ${}^1{F}_3$ and (b) the ${}^1{P}_1$ repump transitions. Experimental data are shown by symbols; Lorentzian fits, by lines. All measured densities are scaled to the peak MOT density achievable with the standard 672-nm repumping scheme.

Figure 5

Measured Ca MOT loading curves for (a) the ${}^1{F}_3$ and (b) the ${}^1{P}_1$ repump transitions, MOT fluorescence is plotted as a function of time elapsed after the cooling lasers are turned on; curves fitted to $N\left(t\right)=R\tau \left(1-e^{-t/\tau }\right)$ are shown alongside the data.

Figure 6

Simplified electronic energy level structures illustrating the main loss channels for the experimentally tested repumping schemes. (a–c) ${}^1{F}_3$ repumps; (d, e) ${}^1{P}_1$ repumps. Here we show only the most significant pathways into lossy triplet states, shown in red. The omitted decays dominantly return to the main cooling cycle. Using only these branching ratios and the natural line widths of the upper states, one can compare the approximate relative MOT lifetimes for each transition. This simple model reproduces the lifetime ordering of the more comprehensive 75-level rate equation model and also matches the experimental results.

Figure 7

Measured Ca MOT lifetime as a function of the $4s4p{}^1{P}_1$–state population with a 453-nm repump. The measured lifetimes are shown alongside the rate model predictions and a curve representing the fundamental limit for any single repump laser scheme in a Ca MOT. This limit is the result of decay from the $4s4p{}^1{P}_1$ state indirectly to the $4s4p{}^3{P}_0$ and ${}^3{P}_2$ states and is found as $0.24/{\rho }_{pp} {\mathrm{s}}^{-1}$, where ${\rho }_{pp}$ is the population fraction of the Ca $4s4p{}^1{P}_1$ state.